Have you checked with Asiana and Korean Airlines? I used them years ago flying from the US to Bangkok.
You can check with some discount airlines but they may have some weight allowances to meet.
Different days of the week, weekends and holidays may cost more. So vary your departure date in order to check for lower fares. Check ahead and behind your preferred date to see if there is a price drop. Holidays, weekends may be more expensive. Christmas time, New Years holidays, and even the Chinese New Year affect the price of a ticket. Summer months from June to September often have higher prices because when the kids and teachers are out of school they fly a lot!
If you are in the US military you may get a hop to Singapore and from there take a train up to Bangkok. The train route is kind of long but not too bad. I did the train from Bangkok to Malaysia (Butterworth/KL) on to Singapore when the airport in Bangkok was closed down in November.