As there are no OW flights AKL-HNL, you would have to go AKL-LAX; QF metal, AA codeshare, and then LAX-HNL on AA. But only one flight to/from HNL allowed, so either pay sidetrip HNL back to LAX, an still count as one segment, or consider AKL-HKG-NRT-HNL-LAX.

With JL flights going down, HNL has become a more difficult destination for XOWE travel.

A realistic alternative is a CirclePacific ticket.