THe Ki-61, as built, would have been a better opponent for later war US naval fighters based solely on performance, Faster, better protected, better diving speed, and still fairly well-armed. Clearly inferior to the Zero only in range and endurance
They problems would arise in restressing the plane to handle carrier takeoffs - and particularly landings. A navalized Ki-61 would probably be heavier as a result and it's performance might suffer accordingly, Also, the Hein was plagued by poor engine reliability, not something you particularly want in a carrier plane.
I like Anime Ninja's idea a lot. Simple and plausible. At the same time the Army places its design orders for the Ki-61 in 1940, have the Navy place a parallel order for a radial-engined variant similar to what later became the Ki-100. In good hands, the Ki-100 was capable of facing the Hellcat on equal terms and the plane could have been entering service at the same time as the Ki-61 - early 1943 - just as the Hellcat was starting to carve up IJN fighters.