Note that LAX-HNL-SYD requires an overnight in HNL while SYD-HNL-LAX has a 3 hour connection.

Also the LAX-HNL is domestic service so no personal video player and the HNL-SYD is a 767 so no 1st class so forget the extra 90 SCs and no lie flat seats which may not be an issue HNL-SYD as its a day flight but the other direction is a night flight.

LAX-AKL-SYD would be a better option as you would have more connection options in AKL and 747 service LAX-AKL with flat seats but again no 1st class.
AKL-SCL you could get 1st class on LA but the inflight service on that leg is pretty poor for a 3 hour 1st class flight.