Try it with the travel insurance first as that will be easier and, if denied, front NZ and demand they cover the costs they have caused you to incur. This is simple tort law and you will win if you take NZ to the Disputes Tribunal. I've done it a couple of times now after NZ tried to dodge it.

It annoys me that their agents still insist on lying about refunds, but the CC isn't ever going to do anything about slapping them into complying with the law on that front.