Many years ago we used to be able to buy an economy ticket for my mother in law, then upgrade immediately with miles. I don't think that's offered much any more, I think you have to bid and then wait to see if everyone ahead of you clears or drops out. Your best bet is to book seats directly with an airline. I just looked at AA from LAX, you can go in July for 60K out and 120K back. There's only lonely return flight, August 29, for 60K but everything in between is at the moment 120K. So that means you could go in business class for 180K miles. You could also check JAL for availability, your AA miles would work for those flights. Good luck!