I think it would be interesting to compare US developments in light of what the others were doing.
The USSR, Commonwealth and Germans all tried to push the enveloppe further after 1941 with things like the 85, 100 and 122mm guns (first deployed in 1943, last two in mid-late 1944); the 17 pounder (proposed in 1940-41), super high velocity 2 and 6 pounders with focus on APDS, 75 L70 and 88 L71 both first seen in 1943.
The US decision to focus new development on a lightweight 76mm instead of a more powerful one at the same weight as the M7 (or slightly lighter only) was meant to reduce the weight of the turrets and tanks able to carry them, possibly immediately fit in the 75 Sherman turret and reduce ammunition size (the barrel was longer than on the M7 to keep velocity the same with a smaller charge). This was particularly consistent with the US focus on super lightweight TDs.
However, in light of the late introduction of the 76 Sherman (dictated by very stringent requirements on ergonomics) and the Hellcat (without even considering to question the emphasis on low weight for TDs in the first place), this type of gun was completely out of place in the 1944-45 battlefield. It is also worth noting that the 75mm lightweight gun and associated light tank were also particularly late, resulting in many complaints about insufficient armament. The next light tank requirements immediately emphasized a 76mm gun of at least the same class as the M1A2 in 1946.
Now, the US was able to get away with this because of the low concentration of heavily armored German tanks in the Western Front directly facing them, logistical problems on the German side preventing said tanks from operating effectively and finally good combined arms tactics to take them out. That said, that does not mean that greater firepower wouldn't have been useful. Using technology to alleviate tactical or training limitations is always useful.
If one actually looks at US tank gun development programs and implementation prior to the 1943-45 (and really 44-45) explosion (with high velocity 90, 105 and 120mm guns), they do leave much to be desired. We only get the 75 M2, M3, lightweight 75mm (not used until the Chaffee), 76 M7, 76 M1 (not used until late 1943) and 90mm M3 (not used until 1944, yet available for testing since November 1942). Meanwhile the Sovs were testing at least two to four flavors of 85mm guns alone.
The 90mm definitely could have been developped from the AA gun sooner AND implemented on tanks sooner, as the M10 GMC could carry it without any more issues than the 76 M7. The technology used for the lightweight 76mm could have been used to either create a new gun or just redo the M7 (new longer lightweight barrel) for a muzzle velocity of 3000/3200 fps instead of 2600 for the M1A2. That is, more or less the class of the 17 pounder. The implementation wouldn't have been any later than the 76 M1 since both guns required a new turret for the Sherman and new hull/turret for the M18 Hellcat. They would just be scaled up appropriately. This option would have been a bit more practical than the 90mm due to the somewhat smaller rounds and still slightly lighter and more compact gun.
Regarding the problem of the manufacturing capability for a new tank, of course one would have to look at exactly what tooling was used in the factories that left tank building in 1943-44, where that tooling went afterwards and what those companies were making afterwards. I still think there was spare capacity in that regard just like there was for the M26 Pershing (or really all the T2X series, these had to be built somewhere after all). Even then, a new tank would surely require some of the tooling to be replaced anyway. I should also point out that there was a serious backlog of Shermans in 1943-44 that were awaiting shipment, so even converting an existing operating line to build a new tank wouldn't necessarily delay deliveries of tanks outside of the US.
Regarding the question of weight, it's an interesting one because after all the US still was willing to develop the monstrous M6, the T14 Assault Tank and the 1945 heavy tanks (with some outright being earmarked for the invasion of Japan), so surely they were thinking the shipping logistics could be worked out, otherwise they wouldn't have made any of these tanks in the first place.
But even if one considered the 40 short ton limit of most dock cranes often mentioned by The_Chieftain, that still leaves a maximum metric weight of 36.287 tonnes. The M4A3E8 (76)W is among the heaviest Shermans and weighs 37.1 short tons (33.5 metric). That gives at least 2 extra short tonnes to play with, and that's before adressing the inefficiencies of the Sherman design.
Redesigns of the Sherman itself were considered but the choice fell on the more radical T2X series. It certainly made sense as these would be the most efficient option. However the rear placement of the transmission evidently led to cooling and reliability problems that weren't seen on the M4 (evidenced by the poor reliability of the T22 that used the same transmission as the Sherman). Much worse, highest priority was given to the prototype with the electric transmission, the T23. This transmission did perform a lot better and was not as hard to maintain as other similar transmissions in foreign countries, but it definitely was ill-advised to prioritize such a radical option in wartime over more conventionnal designs like the Torqmatic and Hydramatic tested in the M6 and eventually used in the M26. Moreso when the latter promising types needed some work to perform reliably.
The sheer inefficiency of the Sherman layout offered plenty of room for improvement even while keeping the front drive. A simple transfer case for the radial powered versions and nothing for the other engines would have allowed a major reduction in hull height (this was done on the M10/M36 GMC hull). Sloping the sponsons were a good option to improve protection there without an undue increase in weight. The Detroit Arsenal proposal for such a redesign allowed it to keep the same weight as the OG Sherman with sponsons sloped at 30° and a simpler hull front. Lengthening the hull a bit to increase the front slope while keeping large hatches should also have been more efficient and would work well with the changes induced by the lower hull. The fighting compartement generally makes an inefficient use of space.
The Australian Sentinel is a decent example of how well you can do with front drive (a simplified M4 transmission even) and a compact engine with an otherwise similar style as the T2X series. The version with a 70" turret ring to accomodate a 17pdr was expected to weigh about 32 metric tonnes with thicker side armor and a better front slope than the small hatch Shermans with the same plate thickness.
HVSS was tested in 1942 on both the Sherman and was seen in 1941 on the M6 Heavy, but the lack of wider tracks for the former and the poor performance of the tracks of the latter on medium tanks meant that it wasn't interesting to introduce them right away. Had there been more interest in developping dedicated wider tracks for a new medium tank derived from the Sherman in 1942, HVSS would have been deployed sooner.
A 600HP+ class engine like the Guiberson T2800, Caterpillar D200A, Chrysler A65 or Ford GAC with adequately strengthened Torqmatic would be desirable and probably even feasible for 1944 but dubious earlier.
IMO even the austere proposal of a Sherman with front drive, HVSS, redesigned hull and ability to carry a 3000 fps 76mm gun without any serious increase in armor would still be appealing for late 1943 production and well within US capability. The front drive placement would avoid the development issues that plagued the T2X series and the HVSS can be made ready sooner than medium tank torsion bars. This is hardly more complicated than the entire Soviet development line from the KV-13 to the IS-2, or the T-43 which was far more likely to fail simply because the Soviets were playing with an even more overburdened hull.
It might even come with a few 'extras' 