Quick update: on arrival into AKL, went to the transfer desk and waited, and waited. We had about 90 mins to departure once through transfer security. One person on the desk dealing with a couple of lads with a BP issue, then two more groups of people waiting ahead of us. Another person joined the desk to help but kept being radioed to go to a gate to deal with boarding an upcoming flight. I don't know if the 1 hour check in cut off was going to apply and the clock was very definitely ticking.

The original desk agent gave up with the lads and handed it over to the new person before leaving to go to do the flight boarding job. As they left they said "if you're needing a BP for NZ105 then head to gate 15, which is a good 15 min walk away". So off we schlepped to gate 15 where the very nice chap said he had no idea why the check in agent in SFO was unable to print the BPs. Fortunately we were departing from gate 16 or else I would have been immensely annoyed at being required to trek around the airport looking for someone to check us in and print the BP.

On the way back, SYD-AKL, the check in agent wouldn't check us in for anything past AKL. This was less contentious as we had a 23h layover but I would have been quite stressed if I'd had the same 90 mins that we burned rather rapidly on out the outbound.