Just search aa.com for MileSAAver award availability. You are most likely to find such availability on JL flights -- at least for the TPAC portion if you cannot find availability on JL nonstops out of JFK.

A Business Class roundtrip from NYC to Japan will cost just 120K AA miles -- with zero carrier surcharges. I would just use the AA miles for this trip, assuming that you can find SAAver award availability. If the JL nonstops from JFK are not available at time of booking, try to find an AA/JL connection out of JFK, not LGA or EWR; that way, if the JL nonstops should subsequently become available, you can switch to it without paying the $150 fee applicable to changing your origination or destination airport.