For this trip, you'll need to compare the purchasing cost of and potential earnings for
1) Buying the trip through United on 016 ticket stock and flying partner airlines
2) Buying it through another source not as a United ticket, and earning based on distance flown.
I'm guessing that #2 will be cheaper, and may even earn you more miles (with 150% on some partners for paid business).
Ultimately you should fly what works best for your schedule. Note that going BKK-ICN-SIN is quite a bit of backtracking. If you could switch SIN and ICN that would save you significant time. On this routing, I'd look to do Eva Air SFO-TPE and Singapore SIN-ICN and ICN-SFO.