There is only one 777 a day NRT BKK and it is always full, or close to it. Flights to SIN generally cost less because there is more capacity.
The answer, as far as I am concerned, is to book way in advance.
The problem just got worse, as Thai Airways cut down its daily flights LAX BKK to 3 or 4 a week.
The long term answer to the qustion is to persuade UA to re-start flying HKG BKK daily. We have been asking for that for a long time, with no result.