The majors may offer deals with those cards when booked from outside NZ, but they will still be more expensive than the local companies. I've always had good results with Omega at both the rent-a-dent and current model levels. They are usually very competetively priced for whatever class you want so long as you book well in advance. RaD Car Hire is another one I've used a lot. Some odd experiences with their cars, but some excellent pricing to be had..