I agree with much of what's been said above, particularly while the British and later Canadian governments weren't exactly friends of Native Americans a massive drive of Independence was a feeling the king was holding back settlement so it's really hard to see how you end up with the Six Nations fully integrated into the war on the side of the US and for that matter then taking part in the Continental Congress in all but the most taken we. However, there might be some ways we can tilt the scales to create more interesting scenario
Step one have a major falling out between the Six Nations and the Crown, this could honestly just be a well timed diplomatic faux pas by a royalist or a disagreement around legitimate settlement, ideally this would also be done in a way that would make the Six Nations a bit more powerful, whether any other tribes nearby who were friendly to the British who could have ended up at war with and conquered by the Six Nations both giving them more territory/power, and creating tensions with the Crown?
Step two make the US weaker, loads of ways to do this (kill off a few key figures early, have a couple of early battles go differently) effectively makes the early Americans more and more dependent on Native American allies, both sides recognise this is a more equal relationship so sending representatives to things like Congress starts make more sense. I know a couple of timelines have mused about a situation where the final peace treaty leaves Britain in control of the south this again feels like it could be helpful as you end up with the effective manpower of the Six Nations much closer to that of the Patriots, forcing a more equal relationship.
Step three keep the US scared, OTL the UK pretty quickly abandoned any suggestion of reclaiming their colonies and despite a couple of flareups the US was largely allowed to get on with its own affairs without too much threat from the wider world pretty quickly this drastically tanks the capacity for friendly tribes to influence things and means the settlement minded founders quickly turn their eyes to forcing indigenous tribes of their land. Now 2 somewhat looks after 3 if you have a smaller US surrounded on all sides by the British I can also easily see the loyalist government of say British Virginia or Carolina perpetually pushing to put down the last of the rebels or even trigger numerous small-scale colonial conflicts over disputed borders this keeps making, the early American government terrified of large-scale intervention by its neighbours and discourages any actions that could trigger an internal civil war or make key allies and swap sides (so in this case groups like the Six Nations, and hopefully creates a bit of a hang together or hang separately pressure cooker environment) especially in the scenario where you've got lots of small colonial wars could also see massive pressure for both sides to acquire as many Native American allies/auxiliaries as possible so this may give another unique role for representatives from the Six Nations effectively going out and coordinating the unions Native American allies, not only does this continue to increase their value and make it harder to justify pushing against their land but it gives the potential for more sources of more Iroquois identifying citizens through bringing some of these allies into their actual physical territory
Altogether I could see this leading to the Six Nations meaningfully taking part in the Continental Congress, and as the constitution, starts to form being able to guarantee their own autonomy to some level possibly ending up as the equivalent of a founding state, while also imposing some of their ideas on the initial thinking about the constitution (I don't know enough about their cultures no what these changes might be). Given enough time for process to become entrenched I'm more optimistic they could maintain territorial integrity (effectively by the time this US is in a position it could safely stab them in the back there firmly seen as part of the establishment), however I do expect you would still effectively see their territories swamped by white settlers just in this case it's people coming from one state to another state and doesn't come with the violent overthrow of the states government. So long-term beyond any constitutional changes they successfully lobby for you likely end up with a situation where one of the peculiarities of the United States is the state of Iroquois, which has a very different state constitution/legal system to its peers, where Iroquois traditions and followers of their traditional religion are protected to some level, where most of the big landowners/influential people can legitimately trace their heritage back to the tribe but where functionally a couple of centuries of internal immigration, and cultural assimilation means the population as a whole look and act pretty Western European, and not that far off from their neighbours.
