So glad to hear that you are safely in NZ, and it sounds like you have hit the ground running!!
Re car insurance, we bought 2 cars while still on VV's, and had no problem getting insurance - Ken used AA insurers and I insured mine through State. We registered my car (which we bought first) using our friends' address in Wellington, and used their address for the insurance too. By the time we bought Ken's car we were already in our rental property.
Good luck with it all - how's the tiredness settling down?
Maggie xx