I attempted to research for redemption on these routes LAX-AKL in business (and airports in between) last year.

My conclusion was that there were either no seats available or very limited seats available. I never ended up finding any strategies that were workable via LAX. There are some opportunities to Australia / NZ via SIN and NRT if you don't go over MPM.

There is a lot of Trans Tasman availability and domestic availability that shows so indeed there is some inventory loaded into the system. It's just not helpful inventory.