Well guys and gals, I'm pleased to report that it worked. On Friday, I checked in my bags and myself for UA 171F, UA 837F, UA 891F, and SQ 72C (BOS-SFO-NRT-SIN-MNL). I got all four boarding passes (SQ's was blue compared to the gold UAs), and the friendly agent at BOS confirmed that since my layover at SIN was less than 12 hours (it's 10 on this itinerary), the bag could be sent all the way to MNL.

In fact, my bag arrived at the carosel in MNL before I did... as the line for immigration was 45 minutes!

By the way, the Transit Hotel at SIN Terminal 1 is great for this kind of layover; for less than US$70, a nice clean, quiet room without going through security, immigration, and customs.