The J2M design actually dates to 1938, it was initially made secondary in favor of the Zero so the first prototype did not fly until about 3 months after Pearl Harbor. Initial engine problems did include reliable output at highest power (hence the earlier question about engineers) but what I've read seems to indicate that this was solved and the need for water-methanol injection made unnecessary before Pearl Harbor. I was unaware of a need for 92 octane gas in the engine though - thanks.Several statements don't add up.
J2M was not powered by a 1938 version of the Kasei, but by 1942/43/44 versions. Kasei was indeed able to make more than 1800 HP, but it needed water-alcohol injection, 92 octane fuel and redesign of engine internals to withstand greater RPM and boost to do so. The 1st Kaseis, as used on G4M that helped sunk Force Z, were good for ~1500 HP for take off, and ~1350 HP at 15000 ft (note that this is winter of 1941/42). Granted, this is still about as good as BMW 801C, with much better reliability and lighter weight, however it is years too late for 1938.
Except we apparently get to use airframes from Reno Air Racers per the OP which makes the scenario more interesting.We are very off topic here. The idea is a panic fighter in 1938.
As I see it, any small nation needing fighters NOW, will buy off the shelf. Forget Aircraft entering service in the next three years do not fit the requirements. Thus, you could choose from Gladiator, CR.50, CR 32, I 16, Buffalo, P 35, P 36, D XXI, M 406, P-11/24, or B 534. Of these, I would lean towards a monoplane with Mercury engine. I would lean towards D XXI or P-11 right this minute, with a projection of adding newer models when available. If money is no object, look into Hurricanes or P-36's, especially if you can get a production license. Train your pilots intensively. Build war stocks. Look at Finland for your example.