Guys, apologies for being clueless, but my heads starting to spin. I want to take my family of 3 to Japan October 12 to 21. Ultimately, OKC to KIX (Osaka) then TYO to OKC. I can go through DFW or LAX. I want to get business class for the international stretches but I'm running into a wall on the AA site - no milesaver business for AA flights, JAL doesn't show up. I tried to figure out upgrade availability on ExpertFlyer, but it doesn't show JAL upgrade availability that I can tell. I've got about 100k miles and trying to figure out the best way to use them.

I can buy miles. That'd get me to about 350k miles with the 100k bonus. Not going to be enough for AAnytime business for 3.
Is there any other way I can work this?