I'll try my reply again - not sure where it's disappeared to!
thanks for the suggestions. Don't have the onward boarding pass, so indeed going out in SIN is non-trivial. I think I'm going to trust uastarflyer :-) and hope that my bag is kept safely for me. Talked to TG again just now, and a supervisor told me that I needn't worry and when I check in with UA tomorrow morning at the transfer desk they'll take care of everything.
So my only remaining challenge is to see if I can get into the T3 SKL with just my printed itinerary. It's worked before, but I'm not confident!