If you have not already bought your LON-SYD flights on Qantas, fly outbound, at least with BA, booking an A380 flight to SIN and continuing on the B777 from SIN to SYD. The connection in SIN is not a problem and the change in flight number gets the two BA flights you need. I assume that your stay in OZ will be long enough for your upgrade in status to filter through the BA IT system