Other Asian, Australian and South Pacific Frequent Flyer Programs - Tahiti to Nadi

Is there any way to fly from PPT to Nadi, Fiji without going through Hawaii, New Zealand, Australia or back to LAX??

Unfortunately, no. At least not based on current schedules.

A connection in AKL makes for the shortest total trip length (at about 9-10 hours including layover), but even this can only be accomplished three or four days of the week.

Is there any way to fly from PPT to Nadi, Fiji without going through Hawaii, New Zealand, Australia or back to LAX??

Yes.

PPT -> NOU (SB) -> NAN (SB). 44 hours, 25 minutes total elapsed time. Leave PPT on Wednesday, arrive NOU on Thursday. Friday in NOU. Saturday flight to NAN.

There is nothing easy and direct, as you have discovered.

Contribution value = 0, but years ago I flew QF on that very route...