What did the AAdvantage agents say when you called to ask about availability?
Try JAL web site.
Try routing via another major city, e.g. KIX, if rules permit.
Try flying out of Haneda.
Ultimately, if you are wanting to keep the LAX-NRT flights, you will either be limited to about half a dozen possible TYO-PEK flights (and chances are reasonable that there's zero availability on them), or you will have to pay for two awards.
And why do you need to start three threads for essentially the one reservation?