I wish I had known about VroomVroomVroom.com earlier. Anyway, I got lucky by getting a UAL discount code for Hertz, which turned out to be $100 dearer on the UA site than by using the same CDP code on the Hertz website. So it's worth comparing with the company sites.
For Hertz (4 days in March coming up at AKL) I am paying NZ$197.28 (AU$157.82) + insurances for a Camry. VVV shows Hertz at NZD165.83, i.e. $8 cheaper over four days, so I'll live with it.
That booking will allow me to put the points on
Virgin Australia, my preferred carrier, even though I used UA's CDP code. For anyone wondering, they are AWD Discount code (CDP) = K019376 Promo code = MUAA125. I am now a plain Mileage Plus member, so it should work for anyone in Australia (for the sake of comparison only -- VVV is cheaper)
The other consideration for cheap NZ rentals is that the cars might be two or more years old. The big brands might have a current model in NZ, as they do in the US, but not always. For Europcar the two cars we were given were one and two years old.
In 2010 we used Europcar for a 3-week rental that cost us around $3000 in all - even today they are NZ$100 dearer for my 4-day rental. We could not take a North Island car on the Wellington-Picton ferry so the biggest trauma in that rental was finding a spot to park the car outside the ferry terminal. All the marked spots had gone and it took an eternity on hold to speak to a human. Luckily he told us to park "anywhere safe" and drop the keys in a slot at the Europcar counter (nobody manning it). That's the kind of situation you can't plan for, but it is worth calling before a trip to see how a cheap company handles those situations.
