Since you are exploring routing via Asia you would need to call AA as CX/JL availability will not show up on AA.com bookings.

If you have plenty of miles then another alternative is to book SYD/MEL-LHR award and then LHR-WAS award and do a stopover in London for a couple days if you desire. You could also try routing through FRA or CDG if you prefer. Note: when I was exploring options a few years back award availability between OZ and LHR was pretty good.

I just did a quick check for 2 award seats and there are both J and F award availability from SYD/MEL to LHR on Jan 1-3 and Jan 8 and onward. Similar availability for FRA and CDG with the exception of a few days. Also plenty of award availability between those EU cities and WAS. Good luck!

I highly recommend Cafe Sydney for New Years Eve. Will cost around $600/person but well worth it is it is in your budget. Reservations open up on July 1. PM me if you want more info.