Wow! I'm blown away by the thoughtful and detailed responses. It's looking pretty tough and confusing, though, to try to do this the way I want. I may be better off taking a roundtrip WAS-SIN ticket with a stop offer in London en route (or, if feasible an open jaw to return from CGK) and then deal with all the Asian travel on separate tickets, as suggested. I'm going to be doing a lot of travel in a new job going forward, so another combination of stops may make the RTW make more sense.
I had thought, however, that I had read somewhere that if you buy a transpacific roundtrip, there are some tour around Asia deals you can add on - does that sound familiar to anyone?