NRT-BKK is always a difficult segment to redeem awards on US carriers.
If you can afford to burn more miles, you could try to get a partner award, especially with *.
If all else fails, consider getting a seat on the less popular NRT-SIN route, and buying a cheap SIN-BKK ticket, a route with wide-open competition.
P.S: I take it you want an open-jaws ticket, as intra-Asia stopovers are not allowed at least on NW and UA, IIRC.