In a word: SUCCESS!
Here's a more detailed report so others can replicate it.
UA checkin agents in San Diego managed to check the bag through to BLR, despite 3 separate tickets (SAN-SFO and SFO-SIN on UA and SIN-BLR on 9W). It took 2 agents and they had to do it through SHARES and to override the system manually a few times, but they managed. They even had the correct dates for the flights: Dec 11 for SAN-SFO and SFO-SIN and Dec 13 for SIN-BLR. It was essential of course that UA and 9W have an inter-airline agreement. The most amazing thing was that they managed to do all this and not split the reservation as we were two passengers on all these reservations.
When we arrived in SIN, we first went to the transfer counter (turns out we had to use Transfer B as they handle Jet Airways; any transfer counter should be able to tell you where to go) and they were able to issue our manual boarding passes. They looked at the bag tag and said it looked right, but it was too early to check if it really made it and suggested we came back a few hours before the flight to check about the bag (we had an 11 hour layover). They also told us that if we needed to check additional luggage (e.g. the carry-on allowance is much less generous on Jet than United) we need to go outside security to the checkin counter. We did come back about 2.5 hours before our Jet flight and the agent was able to call someone and check that our bag was waiting to be loaded onto the plane.
It turns out everything worked perfectly. We found the bag on the luggage belt in BLR and never had to leave the transit area in SIN. We even made it with our overweight carryons onto the Jet plane.