Actually, believe it or not, JAL has 3-cabin service with First class on the NRT-CGK route.

OP, why don't you tell us what dates you are traveling and for how many people? I see LAX-NRT in JAL F from time to time, but without the specifics, its hard to advise you.

Also, if you haven't already, you should call AA and see if any seat is available, and put a hold on them.