The first agent I spoke with when I called today agreed there was no issue with stopping over in Asia before or after visiting Australia. Unfortunately the call got disconnected about halfway through the itinerary though, and then we had to start all over again...

No issues getting the second agent to send OSL-HEL-LHR-YVR-NRT/HND-SYD-SIN-HND-TSA/HND-BKK-HND-LHR-TOS to the rating desk, and they were even okay with booking a BA operated SYD-SIN as a Finnair codeshare (though they mentioned that they usually prefer not to). Finding available flights for BKK-HND-LHR was a bit of a pain because as expected the availability didn't match what I could see on ExpertFlyer, and this cut both ways -- sometimes I would see D0 on EF but the RTW desk could see available seats. We managed to grab HND-LHR as a JL codeshare but only in BA Club World which I was hoping to avoid... oh well, guess I can always try to change it for free if availability opens up. Overall, the agent was professional and very helpful.

So yeah, I guess HUACA is the name of the game. Just waiting for the rating desk now...