Since the Hellcat was considered the unquestioned master of the Japanese planes, the P-39N should have been able to handle Zeros like the Hellcat. Zeros were 330-340mph planes, Hellcats and P-39Ns were 40-50mph faster at all altitudes.
The simple problem with this is airfields. The USN planes had movable ones and the AAF did not. Next problem is range. The 51, 47, and 38 all had the legs so they could cover the distances required and still have station time to fight before bingo (RTB fuel state).
Cheers,
Biff