@sbiddle OP needs to fly AKL-HND, not vv - but a good option AKL-HKG/SIN-HND.

OP. It is up to your TA and LH to try and untangle. Is this paid J or award? Has the journey started? If not, maybe cancel and re-book to suit plans.

The separately ticked CHC-AKL flight is ‘bad luck’ and lost unless you purchased a FlexiPlus fare and so can cancel with refund, otherwise maybe a travel insurance claim. This situation is always a risk when buying separate tickets. Certainly AirNZ doesn’t know your plans and won’t do anything for you.