GHT, I PM'ed you the MPM for AKL, WLG, its slightly over 11,000. So NRT is gonna be a no go.

However, if you route via SIN (and SYD?), IME, you are allowed to go via Europe.

If you make MEL the POT via SIN, its definitely valid. But on the way back you would have to make AKL a stopover and directly home on NZ.

If you need to find dates that NZ non-stops are available, go to co.com, and click off non-stop only when searching AKL-LAX/SFO/YVR.