This is probably blasphemous, especially from me, but having toured the south island of NZ, if I lived in LAX, I'd seriously consider flying NZ Y nonstop to maximize my time there. There is just so. much. to. do.
It's about the same distance is flying coach from NYC to Israel, and I've done that a few times in the past couple years.
If you didn't want to fly Y to AKL, the next best option is probably Plan B LAX-SYD/MEL-AKL.