Now another interesting routing I see availability on (via ExpertFlyer) is on Air Tahiti Nui. AKL to PPT on 12/16 at 4:25pm arriving PPT at 10:25pm on 12/15. You would layover until 7:20am the following morning and continue onto LAX arriving LAX at 5:35pm on 12/16. It's in Business Class - you'd have to call AA to book this one. Flight numbers are 102 and 8, respectively.