Air New Zealand no longer has its own flights between LAX-PPT, and the one you are seeing is an ATN code share; i.e., you will be flying an ATN flight on an ATN plane.

Taking ANZ flights from LAX-->AUK--->PPT is quite the long way around, and probably doubles your flying time.

Air Tahiti Nui does have some red-eye flights from LAX-PPT, but only specific days of the week. The schedule changes by season, and it's too early to tell the schedule for May 2013, but, for example, in May 2012, the Sunday night TN 111 leaves LAX at 11:30 p.m. and arrives in PPT at 5:30 a.m. on Monday morning.