Since the FESZQ fare is very restrictive and you need to visit India first, your routing seems to be the best way to maximize your time in SQ F.

If you chose the all-J SIN-LAX SQ nonstop, there wouldn't be any surcharge but you would be downgraded to flying J.
If you want to maximize your F experience, I'd consider either of the two one-stops to the west coast:
SQ 12: SIN-NRT-LAX (currently) on a 744.
SQ 2: SIN-HKG-SFO on a 77W similar to your IAH-DME leg.