I would have set up an NZ banking account from overseas while we still had a permanent address. Proof of address using short term housing (a holiday home) proved to cost us a lot of time calling every bank in town before we found one that would accept our proof!
Most of the banks had a problem with the fact that we were on a visitor's visa for only 6 months (one bank said a 12 month one would be ok, such as those from Commonwealth countries can get). Those that were fine with the visa, by and large, didn't like the "holiday home" proof of address letter from the property manager. Even the library made us get a "visitor" account instead of a free one.
However Nelson Building Society was ok with all that, and I talked to someone as ANZ that also was fine with it. It seems to depend partially on bank policy and partially who you happen to talk to. One lady insisted the bank would lose their license if she accepted our proof. Whatever, we did the legwork and it finally happened. We are kind of a special case since we don't even have a real home address overseas anymore, or we could have set something up as a migrant account using our old proof of address, according to BNZ.