I would definitely ask them to check biz class on Singapore for you. I did this a couple years ago to travel IND-HKG and PEK-IND. Had to take a couple of weird routings (like PEK-SIN-LAS --that's right, SIN-LAS -- on my return) but the SQ biz experience made it easy.

You'll probably have to get to SFO on DL in coach to connect with the SQ legs as the reward tickets to Asia require routing via the pacific.

Good luck.