I went to a private lodge in Zululand called Zulu Nyala:
http://www.zulunyalaheritagesafarilodge.com/. It was a great place to take photos and see animals, but you're not shooting anything there.
I didn't quite understand the model, but I think the market is something like this. You have the big national parks and you can go there. You also have smaller private lodges, where they may own 500 acres and buy or breed animals that have smaller ranges. The animals run wild, so other than an occasional fence you don't really see any difference. And then some animals with big ranges will hop the fences and wander throughout all of the places.
The place I was at had basically every animal on it other than the big cats. The lions never came onto the private lodge, but leopards would come in and out. Monkeys and birds paid no attention to fences, and occasionally wildebeest or zebras or things would jump fences and wander around. I don't think they worried about the more common animals, but if a rhino got through a fence they'd go fetch it somehow.
I think these places are near the bigger national parks as part of making a big rangeland, so we took an excursion to a national park to look for lions one day.
If you're wanting to hunt a leopard, I'd think that you're either going to spend a long, long time waiting for one, or you're going to do the sleazy thing of shooting one in a cage. They're not easy to find, and I don't know if you'd be looking on the private lodges where they're moving from place to place, or the national parks. It doesn't seem like a good use of time and resources when it'd be more entertaining to spend time observing animals. But then again, I'm not a hunter type.
I should note that South Africa did not feel like a third world country at all. It felt more like wandering around in Europe somewhere.
I went to Madagascar while I was in the neighborhood. Most commonly, people would combine a safari with a trip to Victoria Falls or a trip to Cape Town, but I thought Madagascar was quite interesting. I'd love to go back to both countries and explore more.