If I understand you correctly, you're suggesting between February 1938 & February 1940 the prototype aircraft couldn't have been rebuilt to take the power of the R-2600? The prototype was rebuilt several times while Grumman was trying to compete with the F2A Buffalo. Respectfully that's what a prototype is used for. The great fighters of WWII were built around their engine, the engine wasn't picked to fit the protype. General Motors had little trouble building the FM-2 version with a more powerful engine, and new tail section. It was still able to use the same wing and landing gear of the F4F-4.
It is not the power I have problems with re-building the Wildcat prototype, it is the weight spiralling up severely due to the jump from the initial 1-stage 1-speed S/C R-1830-SCG the XF4-2 used. That engine was 1370 lbs, and was replaced with the 2-speed 2-stage S/Ced R-1830-76 (weight 1565 lbs) for the F4F-3. For comparison sake, the R-2600 as used on most of A-20s, with 1600 HP, weighted 1950 lbs.
The 10 ft prop (314-315 lbs) will not cut it, will need at least the 11.3ft prop like the A-20 used - 400 lbs?
(the FM-2 used a 394 lb prop)
Oil system (30 lbs on the -3, 35 lbs on the -4, since it was supposed to use drop tanks) will not cut it, half of the oil system for the A-20 = 172 lbs (for 344 lbs total); the FM-2 went with 99 lb heavy oil system. Oil itself on the -3 was at ~70-80 lbs, we gonna need 100 just to cater for greater power?
Engine bearers, firewall - perhaps another 100 lbs?
So after we're past the firewall, weight is up by ~550 lbs, or about extra 10% of the empty weight.
Extra fuel tankage (140-ish US gals will not cut it anymore, 200 just might?) = 360 lbs + another 100 lbs for the self-sealing fuel tanks (it was 233 lbs for the fuel system on the -3, more on -4).
Sturdier U/C, since the old, 351 lb unit will not do - another 50-100lbs (FM-2 U/C was at 442 lbs). New U/C will need longer legs and wider tires, too.
We didn't added any ballast to the tail yet, and we didn't increased the tail yet.
If we don't touch anything else, we're at a 1000 lbs greater weight for a clean and fueled 'Chad Wildcat', ie. at 8500-8600 lbs instead of at 7560 lbs (full ammo for 4 HMGS, full fuel, still no folding wings). Now we enter the problem of aircraft not being able to match the same G limit as the -3 did since the strength (and also the weight) of the structural elements remained the same. We also don't meed the stalling speed requirements that -3 meat easily, since the wing loading just went up by 15%. Both of the problems are made worse with desire to have the folding wings and an extra pair of MGs for the next version of the Chad Wildcat.
FM-2 was powered by a
lighter engine than the engine on the F4F-3 or -4 (1400 lbs with accesories for the R-1820-56), that meant the FM-2 weighted as much as the F4F-3 despite the FM-2 having the heavier, folding wings. Increase in power was modest, 1360 HP vs. 1200.
I agree that the fighters were designed around the engine. Problem with the F4F was that it was designed around a relatively small and light engine.
In 1938 Grumman wanted to exploit the power of the R-2600 and could modify the airframe with little trouble, after all they had 2 years to do it in.
Would they be better advised to modify the XF4F-2 to have the R-2600, or that they make a bespoke aircraft with the R-2600 in the nose?
The issues you raise about the turbo charging are more relevant. High altitude performance would depend on what Wright had available in 1940-41. General Electric led the way in WWII with its Superturbochargers, perhaps they could've helped out in improving the high-altitude performance of the R-2600 like they had on the Wright R-1820 engines on the B-17. It's not like this was an insoluble problem.
For their own reasons, USN was never really sold on turbochargers. They did support (not just in wording, but also monetarily) the work at P&W to make the 2-stage supercharging a viable tech; I assume that they also supported the similar work at Wright, that was later than P&W by many months in that regard.
A fighter that also has the turbocharger required to supply the compressed air at 20000+ ft for the R-2600 will add both weight and drag penalty, so again I'd say we're better off with a bespoke design.