I know this isn't quite what you want, but what I did in my mod was give Japan an 'advanced fighter' as its special unit. I think I read somewhere that only 18 Kamikazees ever attacked, so it doesn't seem to be an essential to being historically accurate -- and, with all you've said, might be hard to set up right.
I increased firing rate, gave it a larger operational range (from 4 to 6), brought up its offense but kept its defense at 2. Movement on 2, if that matters, up from 1. Haven't tried this all out yet since I can't set up my world for it to work the way I want.
Put shield cost at 7.
So, basically, cheap offensive air unit, but low enough defense that it's vulnerable if you don't come in high numbers. Sort of works out historically, I think.
Did some tweaking of America's unit, took away F-15 gave them B-17 (i'm not familiar with the right model of the US's best bomber of the era, sorry) -- but, basically, really great bomber -- big range, lots of bombard capability, good defense, can carry tacticals.