If you book your next trip to the UK as a revenue booking on the BA 15/16 changing to the 11/12 at Singapore this will give you four sectors from one return trip to the UK, and more Avios/TP than the 15/16 all the way through. Maybe not much help to get you one more sector this year but might be useful in the future?

FWIW, I would stick to BAEC and not change to Qantas as your main FF scheme. For a second FF scheme check out Virgin Australia Velocity (which you can get a points earning credit card for in Australia fairly easily) or Etihad (which gives benefits on VA).

If you still have access to a UK address (family etc) it is worth keeping a bank account and any Avios earning credit cards ticking over if you are sticking with BAEC.