I've also seen this behaviour, with the issue being phantom or stale partner inventory used by google. The only solution if sticking with google flights and united is to try swapping out partner flights and see if you can get one that will ticket. For example, you can try
https://www.google.com/travel/flight...iKRDY4MLHg4nFA (changed last segment from LH1400 to LH1402). Unfortunately you have a pretty complex itinerary put together, so it may be quite a struggle to find an alternative, especially if the issue winds up being with the once/day NZ flight instead of one of the LH flights.