We didn't camp in NZ but we saw many campgrounds when we toured there when we didn't want to go to USA in 2017. They're relatively primitive but well maintained. I wouldn't mind RVing in NZ; right after we do a motorcycle tour there.
No problem driving on the left as DW is ex-English and I've driven in England many many times, but we did hear of fatalities caused by foreigners driving on the wrong side of the road.
I don't know what this gov't red tape you're talking about is. We didn't have any. We did a self-drive LoTR tour (FANTASTIC!) so we had to rent two cars. No problem.