One of the best ways to check availability on oneworld airlines (which are partners of American Airlines) is to use the British Airways website. That’s because BA.com shows the most partners online — including Japan Airlines flights that are not available on the other good site for award searches, Qantas.
Unfortunately the British Airways site is given to ‘break’. It will either not show entire airlines (for awhile US Airways flights didn’t show there but fortunately those show at AA.com!) or will show ‘phantom’ award space, it will appear as though awards are available but in the end the space isn’t bookable and will error out at BA.com (or if you call a partner airline, you’ll be told the space isn’t available).