Rodney,
Ann and I spent time last April hunting with WildernessQuest. I started out free-range stag - saw nothing for several days and then opted for estate 360. Accommodations are great, you eat your meals in your cabin with your guide - ours was Jimmy. We then did helicopter in for Tahr. Got a nice one then had a storm come in and were stuck on the mountain for 2 1/2 extra days. Zion paid for flights for us to catch up our itinerary (not expected and wasn't their fault - that meant a lot to us) and Jimmy drove us to the Christchurch airport.
We saw multiple fallow deer - both free range and estate, but they were not on my list. And, lots of sheep - Ann just wouldn't let me shoot one, but I was very tempted.
We didn't know this before, and I'm not sure if would have made a difference, but it is run by the Gloriavale community. Nothing that was an issue. If you want to PM me, we can discuss further.
John