Maybe MEL-LAX-SFO-YVR-JFK//LGA-YYZ-DFW-YVR-LHR-JNB-SYD-PER-ADL-PER-ADL would be doable - use QF's SFO-YVR service (in season) and CX's transcon to JFK (lunch flight eastbound v. dinner/redeye westbound.)

Of course you'd still be leaving 6 segments on the table, some of which could be okay for mileage - JNB-MRU-JNB for example, or LHR-DXB-LHR etc. Your call.

Edited to add - BTW, about AUD675 cheaper if bought/begun in NZ, but obviously fewer Oz segments.