If you want it all on one itin I think you really narrow the field, since only a few alliances (like Star) would have all the pieces and no single carrier could fly its own metal the whole way. Something like UA/TG could do it, but I doubt they'd be a price leader.

If it were me I'd look to break it up into pieces. BKK-CNX can be done on Nok or Air Asia, and Air Asia even does KUL-CNX if looking for an alternate gateway.

LAX-BKK and SFO-BKK are usually the baseline on lowest fares from the U.S., as those routes also have the Asian carriers like Eva and Korean competing. Often those less computer-savvy airlines are the last to fill and are the price leaders. If RDU-BKK is pricing at $300 or more higher than the lowest SFO or LAX-BKK then it's probably due to less competition. I've had several cases where I've flown on a different ticket to a U.S. gateway because the gateway had much cheaper tickets and it more than made up for the cost for the separate ticket to get there. YMMV.