Call UA , see if they can handle a 5 leg bag check.

At Thailand, it may be that you have to claim your bags at BKK for customs. Making this a 4 leg check.

If layover at SFO is long enough, I would check only to SFO, the recheck direct to SQ.

If a bag get's lost, it's the last carrier responsible for finding it. A UA bag tag issued at MSY may be harder for TG to find than a SQ bag tag issued at SFO.