You are not doubling back from PER. The SYD-PER-MEL routing is legal.

ICN-NRT is a separate purchased ticket not part of your OWE ticket.

The only alternative I can see to the NRT-SJC-LAX route is to do ICN-HKG-LAX. In that case, you must book the AA codeshare on CX out of HKG. Remember, you do not get AA mileage credit for M fares on CX coded flights so you must book the flight as the AA codeshare. Of course, this also saves buying that ICN-NRT ticket.