Does anybody here have any experience with the "starting a business in NZ" residence visa process?

At least one director of a NZ company must be a resident of NZ or AU
 
hrmm, it looks like "resident" in this instance just means "lives in NZ", as distinguished from "permanent resident", which is harder to do

I didn’t go through the entrepreneurship visa process, but when I applied for permanent residency the strategy was to apply for a two year work visa at the same time as applying for residency. The work visa would come through quickly and the residency visa might take up to two years to come through. In my case it only took about six months and I got the distinct feeling they took my application and processed it, sat on it for six months, then came back to check if I still met all the requirements before approving it.