Consider LAX/SFO to/from BNE/SYD/MEL. Only QF flys LAX-BNE non stop. You do not need to fly to/from the same airports out & back. Book as one ways. Also consider Fiji Airlines.
Keep looking before you pay the high aanytime awards
This: Fiji can get you 90% of the way there in relative comfort for very few miles in some cases. The inclined lay flats aren’t great, but have one of their signature PDB (or two) and it works out good enough to get 11 hours of rest IMHO