Another option is to get most of the way there on SkyTeam and finish it off with another carrier. NW can get you to BKK from NRT, which you can get to on NW or CO from the USA. You can then connect to AF (which is an all-SkyTeam routing) or any other carrier at that point for the short hop BKK-SGN. Or EWR-HKG on CO and then a slightly longer hop HKG-SGN on one of the many carriers running that route.