Ia Orana from Tahiti !

Indeed you will have the choice between Air France and Air Tahiti Nui to LAX and Hawaiian Air to HNL.
In your case Air France will be your only choice. We operate 4 flights a week departing LAX on Thurs/Fri/Sat/Sun at 22h05 and arriving in PPT at 04h30. The flights to LAX from PPT are departing every Fri/Sat/Sun/Mon.
You should be fine with nonrev tickets as June is not a vacation period in Tahiti.
Should you need loads please do not hesitate to ask.