I've noticed that any flight booked through the AirNZ website or app will allow payment with Airpoints dollars only if the flight is all on AirNZ operated aircraft.
If, for example, the flight is AKL to Miami via Houston and 2nd leg on a United operated flight, that the pay by Airpoints option disappears. I thought that Airpoints dollars could also be spent on partner airline operated/AirNZ ticketed flights booked through the app?
So... another option is to book an award flight through a Star Alliance partner for that second leg, with the inconvenience of having to re-check baggage? Ok, so looking at this page:
Huh? An Auckland->"North America" flight is 750 airpoints dollars? That's quite a bit cheaper than Air New Zealand... especially if the flight is to Miami for example. So maybe better to just get a United ticketed Star Alliance award flight the whole way?
As this particular trip isn't until April 2019 I can't book it yet so am a bit ahead of myself!