I have no personal experience to compare first-class service between airlines and flights, so the following is a very unqualified suggestion, but if mileage maximization is a subgoal and a extra flight hours is not a concern, perhaps making SYD-NYC on QF, LAX-LHR or YVR-LHR on BA, LHR-HKG on CX, and HKG-SYD on QF as the transcontinental legs would be worth considering. Or HKG-AKL on CX if they haven't been to New Zealand.

The itinerary in your original post isn't valid as it enters Asia twice.

And Katoomba is indeed a lovely place (even when it's raining and misty like it was when we were there in June -- part of our DONE4).