I've taken a 3min gander at the dual tax agreement and it sounds like your standard foreign tax credit situation. Whatever tax you pay to the US will be a tax credit for NZ and vice versa.

So, you'd basically run the company in the US according to the same rules as everyone else it seems.

International tax is not my specialty so I'm not going to pretend to be a pro. If I had more time, I could probably give you a better answer. Sorry!