On some of my trips to NZ and AU we shot "culls" for a very cheap price, it greatly added to our overall hunts. One place we hunted in AU had two mature red stags with 30 to 36" spikes, one of them had gored a quality stag so they were going to get rid of them, we were able to shoot them for a couple hundred dollars. I'd ask about shooting a regular stag and how much extra for the extra cull?
Plane tickets are one of the largest expenses, on my first trip to NZ I only shot a red stag and a goat. After getting home and realizing that I wanted to do a lot more hunting in NZ and AU I decided that on future trips I would shoot as many animals as I could possibly afford and make the most of each trip. I also started planning hunts in NZ and AU back to back, the plane ticket from NZ to AU is far cheaper than a ticket from the US to AU.
Some of the funnest hunts were small game, I don't know for sure what you can still do at night, but you could ask your guide or call DOC. When I was hunting NZ you could hunt almost anything at night on private land. We hunted fur possums and wallabys, also hunted rabbits and hares, what a blast and many landowners are happy to have you come and hunt these pests. We would go to town and ask around for landowners who might let a person do some pest shooting.
I called the Dept of Conservation (DOC) before each trip to verify what we could do ourselves and would plan a lot of our own hunts, we sometimes did more hunting on our own than with guides. In NZ we hunted tahr, chamois, red stag, wallabys, possums, hares and rabbits, wild goats, non-native birds, and went fishing on our own. A couple times we chartered a chopper to take us tahr and chamois hunting, that is an awesome experience. We were not always successful on every one of those hunts but many times we were very successful. It worked well to rent an SUV at the airport and tour both Islands hunting at various locations along the way. We did a lot on our own and would also have hunts planned with guides at different locations on specific days.
I haven't been over there for quite a few years, but you could call DOC to verify what you can do on your own to add some extra activities to your trip at very little cost. I'll also add that NZ is safer and friendlier than the US, its safe to go anywhere there on your own.