Welcome to FT kgilby

While I find that Cathay is my preferred airline USA --> PER, adding Maui on the return makes that problematic. Leaving QF as the likely OneWorld option. Issues in finding DL ticketing options is an exercise for others. And OW circle Pacific tickets will be relatively expensive but might be worth checking.

Consider LAX-xxx-PER (where xxx = BNE/MEL/SYD) on the inbound and
PER-SYD-HNL-LAX on the return with a separate ticket to Maui. You can try the QF online multi stop option though I think a travel agent might do better.

If flying discount economy explore adding ORD-LAX to the ticket. In premium cabins likely to be less expensive with separate AA tickets ORD-LAX. And perhaps HNL-ORD.

Happy wandering and let us know the outcome.

Fred