Agreed. But this is where your hypothetical exercise needs to begin.
Otherwise, as I wrote above; in a sea of Wildcats, Hellcats and soon Corsairs, they'll be no Merlin naval fighter for the USN.
The USN didn't begin to operate Hellcats and Corsairs in any number till mid 1943, that's very long time from Nimitz's request of June 1942.
Nimitz's telegram seems to be going a long way to say a couple of things:
1. We need Army planes for the land based Marines so we can put all available Wildcats on carriers. Okay. Not that there were any Army planes available in June '42, but not impossible depending on the number of land based Marine squadrons.
2. We need to lighten the Wildcats and increase ammunition capacity. Okay, that could have been done immediately aboard the carriers. Remove two of the six guns and put more ammunition in the Wildcat's four remaining ammo boxes in the wings.
Converting P-40s for carrier use may have been an impossible job. Folding wings, tail hook, big weight reduction (P-40F weighed 8500#), strengthened landing gear and who knows what else.
Corsair didn't get into combat until Feb '43 and that was for Marine/land use. Hellcat didn't get into combat until fall of '43. Probably could have had the Corsair ready for carrier use before a reworked P-40.
There was no shortage of F4F-4s in the Pacific, especially given the reduced number of carriers available to the USN.
There were field mods to reduce guns to four and increase ammo, but the net result was that TO weight remained the same and there was no increase in performance.