NZ’s online system isn’t flexible enough when something goes wrong. It doesn’t seem
to have the ability to offer your nearby ground alternatives.
The call centre is usually really good if you get the right person, and tell them the replacement flights you want to take.
E.g I have a 12hr delay on AKL-OOL before, a 1am call to the call centre got me rebooked via SYD and there only 2hrs later than planned.