So maybe all we need is some small cultural social tweak which results in Llamas proliferating much more widely.
What does this matter? Well, it'll change Andean societies, and that may have knock ons all over, including contact with Meso-America. And you might get more robust or specific-environment tolerant Llamas that will transfer to Meso America.
What do you mean by this ? Just to clear something up if you mean they don't adapt well to other environments we have lots of evidence of llamas living in the Peruvian coast from huaca de la Merced or the 200 sacrificed ones in near the beach of Huanchaco by the chimu llamas are also found in Machu Picchu were the jungle stars not saying llamas would survive the Amazon or Yucatan jungles but they can survive in more than just the higher ie 3000 m areas of Peru
I understood mainly from this thread itself that tropical humid climates would distress and then weaken and kill Altiplano llamas pretty quickly, so that I suspect the secret of Empress Josephine's little pet project to bring some to France might have only partially been being able to choose a route with somewhat less cumulative exposure to tropic humidity, but also related to accelerated travel along the routes that cut down the time the creatures had to run that metabolic gauntlet.
If in fact OTL we have breeds, populations, of llamas that can survive, breed and work in lowland tropical coastal climates, then it somewhat changes the timing and nature of DValdron's suggestion. Then we'd have to ask, why did these tropic-adapted llamas not get adopted for regular use all along the coast, and thus be available for gradual cultural diffusion of this regular use northward to Panama and thus across to the Caribbean coast, all along the northern South American coast around to northeastern Brazil--not to mention populations brought over the ridge of the Andes eastward to the northwest Brazilian Amazon basin and thus down the rivers to that same northeastern coast by that route. If their use is established all along the northern tier of South America, never mind their spread back toward the equator and beyond down the Brazilian South Atlantic coast to the pampas, they ought to continue to be adopted up both coasts of Central America and Mexican Mesoamerica until we get to latitudes where some combination of worsening aridity and cold snaps presents them with a third environment.
But this third environment has some semblances to their ancestral situation in the Altiplano. There too, the air is generally dry and temperatures range from very hot to quite cold. At this point, if the herds adapted to lowland tropical hot and humid conditions retain a fair amount of genetic diversity, some of their offspring should be tending to show ancestral traits--these are selected against by remaining in a tropical environment, but on the edges the disability this reversion tendency would inflict on the individuals in a tropic setting would not leave them at the same disadvantage and they would become more favored in a climate that in some combination fluctuates to colder, or tends to be dryer.
In fact looking at climate geography, there would be two broad divergences in fourth and fifth directions--some herds operating in conditions not too dissimilar from the ancestral Altiplano, in Mexican highlands, would border on more and more arid land and tend to be selected naturally for features tending in the direction of actual camels. Their pre-adaption to the Altiplano ought to help them here insofar as it recurs. It might be they cannot adapt beyond a certain point, not on the time scale of human breeding practices, and their use becomes rather more marginal, but stretched into the more adverse zones by careful practices of the herders.
Meanwhile other tropicalized herds will spread along the coast of the Gulf of Mexico, and there further adaption is a matter of becoming more tolerant of cold winter conditions. Right on the OTL USA Gulf coast, conditions are often for much of the year pretty similar to somewhat cooler tropics, still pretty hot and humid, but with cold fronts coming down off the Mississippi valley and the Great Plains beyond in midwinter that can bring waves of subfreezing temperatures along with severe storm conditions. Here again, some reversion to Altiplano strengths involving cold tolerance, probably at some cost to their ability to stand extreme tropical heat (which they need to retain to tolerate hot humid summer conditions to be sure) can reassert themselves, resulting in a North American temperate zone tolerant breed, or families of these variations separately adapted to various regional climates, slowly filtering their way toward the Great Lakes region up the Mississippi system and along the Atlantic coast toward New England.
On the west coast, we go from very tropical conditions in Central America toward somewhat cooler on annual average, and much dryer, conditions approaching Sonora and Baja California; breeds that can gradually adapt to the arid west coast (and thus slowly filter in to the southern reaches of the very dry Great Basin) can eventually reach the wetter California coast around Santa Barbara and beyond. Going inland over the coast range ridge, they and their herder humans find the Central Valley; if they can adapt to its western slopes they can cross the central river streams and go up the west face of the Sierras, at which point they are again coming into environments pretty similar to their ancestral Altiplano, indeed another stream of spreading llama use is likely to take up breeds re-adapted to the Mexican highlands and be coming up both sides of the Sierra ridge reaching to places like the Lake Tahoe-Washoe County region around Reno and Carson City of OTL. Another path has already been alluded to via the Pueblo peoples adopting Mexican-highland readapted breeds, and from there, over a gradient of increasing cold, I would think they'd reach up to the Great Salt Lake area as well as the east face of the Rockies, while a northern Great Basin adapted branch lightly fills in the more fertile regions of the inland Northwest states--Colorado, Wyoming, Montana, and Idaho.
Meanwhile the coastal branch along the Pacific can gradually filter northward past the Golden Gate, up toward Humboldt Bay and beyond to Puget Sound, while inland the basin-adapted breeds largely reverted to Altiplano baseline fill in the arid inland zones upriver, and the populations on the east face of the Rockies gradually filter eastward into the upper Great Plains and meet up with populations un-tropicalizing from the lower river courses, and also insofar as populations coming straight north up the rivers fail to fill in the Great Lakes zone from the south, branches from the west will fill in there west to east.
Whenever different fronts of this expansion meet from alternate paths, we will have interbreeding of the herds with the resulting genetic reshuffling providing newly exposed variations that give opportunity for new hybrid variations to establish themselves, while increasing the general genetic diversity of both border populations for general vigor.
Can they ultimately wind up somewhat prospering on the northern plains and even mountain ridges facing the Arctic Ocean?
Some questions have been raised about how useful llamas actually are to be sure. Apparently devising some kind of harness to allow them to pull traction loads, whether for pulling travois or wheeled carts (or hauling river rafts from the shore) or plowing, is not easy and perhaps not usefully possible; we can't be sure from the fact that no such inventions happened OTL that it is impossible, because the horse collar for instance took a long time to be invented (or adopted, if invented elsewhere) in Europe. But setting such a possibility at naught, along with the possibility of breeding bigger specimens that can be ridden by adult humans, we still have at any rate their use as pack animals, and I do think that would offer useful possibilities to humans in various stages of society.
This path of development is not something that would be driven by elite command--broadly speaking. We should not be looking to chieftains and kings adopting them for prestige nor primarily for use in combat, though surely if working llama herds can be established for daily work uses some individuals can no doubt be trained for use by armies. Unlike war horses or camels, fighting forces with llamas in hand would not want to send the beasts into direct combat; their use would be to carry supplies and items of kit that might extend the ability of a given force of fighting men to range farther and perhaps faster from bases to strike at their foes perhaps more quickly and perhaps in greater force.
"The elites" after all aren't any more uniform in social composition than the commoners. The ones we hear about historically will tend to be chieftains and would-be kings and emperors to be sure. But among the non-military classes, overlapping them to an extent, will be traders, and the basic premise of the divergence here is that in the Andes at any rate, there is more of this kind of activity providing a greater number of more work-adapted llamas being used more intensively in the ancestral Altiplano. Insofar as greater trade volumes translate into greater overall wealth, the societies that adapt best to these opportunities enjoy an advantage, and that means they will tend to be societies that give more prestige and listen more to the interests of actual traders. To a great extent if a given chieftain has ambitions, they will be required to give more heed to the input of persons who boss trade expedtions, and must to an extent be part-time warriors since ancient trade missions tended to be adventures into territory controlled more or less by societies other than the trader's own home base society. Traders cannot depend on established rule of law to protect their goods and themselves, they must be able to defend themselves on their own hook--and therefore able to impose their own wishes by threats of violence backed up by the occasional demonstration. Locals who cannot resist such subjugation will be absorbed into more or less colonial subordination; defeated groups of this kind might well look for chances to turn the tables, which will probably involve adopting some llama herds of their own, and either fighting better with them to drive out the invaders, or anyway balance the score of combat so the invaders must revert back to fairly peaceful trade, or using the better mobility to flee away from the strongholds of the invader-traders and thus disperse lessons learned from the contact over wider areas. If we have peoples building strength on strength by a combination of successful subjugation of some populations and negotiating trade relations with others, who therefore can muster more strength, the most efficient application of that strength would tend to be favored in the long run, which means elite commanders either emerge from the ranks of trader-adventurers, or learn to incorporate them into their forces, which means listening to their lore about facts on the ground.
Setting aside the matter of innovation forced by violent threat, I do think pack animals becoming available would have some positive attraction to all sorts of peoples even with no spears pointed at them. Expanding populations of the peoples who had previously adopted llama variants domestically will be one component of expanding llama uses and llama ranges, another would be piecemeal adoptions by native peoples who can see some of the advantages--and might underestimate the costs involved, slowing the process as various debacles discredit the adopters and leave them weaker, but the learning curve will tend to develop expedient trade-offs that leave them better off overall, less so in climates more adverse to the llama breeds on hand, more so as these adapt to the changing environments and human herding practices evolve along with this.
So--if we have truly tropicalized llama breeds on the South American Pacific coasts, I don't offhand see why they did not become ubiquitous, in very heavy daily use, all along those coasts OTL. I am guessing it is because the OTL coastal herds were not really properly adapted to prosper enough to be very useful there. If that is true a deep time POD of more intensive Altiplano uses might possibly enable the eventual development of a truly fully tropicalized breed, perhaps. If the explanation of the limited spread of such actually accomplished OTL is otherwise, we need to track that explanation down and account for it somehow.
Either way, I think the key is clearly getting that tropicalized breed established on the tropical coasts of western South America; from there I suspect if this happens early enough, the way is open for tropicalized llamas to be spread throughout the entire range of humid tropics in the Americas north and south, roughly from the latitude of the northern shore of the Gulf of Mexico all the way south to the latitude of the Pampas in the South American cone.
In addition to likely outcomes of multiplying human productivity in at least the lower Mississippi and southeast tier of the OTL USA, and more ancestral types doing that in the west up to British Columbia and Alberta in the west, we'd also have tropicalized llamas filtering into the Orinoco and Amazonian river valley systems. And that is just from the second wave of llama breeds beyond whatever improvements happen in the Altiplano, from the tropic-humid variation which is key.
We get the OP specification if the second trend of variation, basically a reversion of coastal tropicalized llamas back to Andean type conditions in the Mexican highlands can go forward soon enough and fast enough on sufficient scale to establish a secondary highland population. Strictly speaking there would be no need to then bring Andean individuals north across the tropical belt. However if the greater general trade intensity based on using tropicalized llamas enables it, perhaps it will consciously occur to Mexican and other northern breeders that bringing in breeding stallions (or whatever the proper term for a male llama would be) from the Andes directly will improve their breeds moving into the northern highlands, and projects to purchase or otherwise obtain some young males just after they are weaned and bring them through the tropic gauntlet to reach the northern highlands and breed there upon reaching maturity might well be attempted. If they can be brought to the Mexican highlands, it would be possible for such breeding stallions to be brought further along to places pretty far north. It might also be possible, given faster boats of greater capacity and more or less reliable sea routes, to forward some Altiplano breeding stallions to let us say the southern reaches of the Appalachians, in northern Alabama and Georgia up to Tennessee and Kentucky and gradually occupying the upper ridges all the way to Canada, then if coastwise spreading has not populated the Atlantic and Great Lakes coasts, for them to filter back down
But none of this climatic leapfrogging by conscious human directed long range breeding programs is strictly needed, if we have a tropicalized population and time enough for diffusion from one viable range to another.
If it is categorically impossible to get a lowland tropic-humid climate tolerant breed, I suspect we get OTL outcomes and limits, and it does seem likely to me this is what actually happened OTL--if this is the case, to get an ATL along these lines, we need a deeper time divergence involving an ATL population of llama variants not found OTL, and if we are to call the critters serving as the tropical-llama variant "llamas" at all, they have to be able to interbreed with Altiplano llamas, otherwise we are proposing an ATL animal species that either never evolved at all on Earth or did so but then died out. Perhaps it might be a matter of a breed that was killed off by early waves of human hunters exterminating them by overhunting in their native range OTL managing to hang on and avoid that fate in the ATL, to be taken up by human breeders at a later date.
Such a deeper time variation might be ruled by site rules to be ASB as an evolutionary POD; if we could show there was a suitable candidate for cross breeding or hybridization with OTL highland llama breeds which did go extinct OTL about when humans first invaded their bioregion, we could affirm this is a human historical POD and Pre-1900 is the right forum, otherwise we'd be sent over to ASB where we might as well suggest some kind of elephant or ground sloth or what have you instead--or stick to some camelid plausibly similar to llamas more conservatively but still formally ASB.