Why can't one simply travel to South Africa, rent a car and go to the game parks yourself? The parks have plenty of accommodation, and you can book safari trips with the parks themselves. The major supermarkets are loaded with products with the South African Beis Din kashrut symbol? I think it's outrageous how much Safari operators charge vs. how much the locals pay for the exact same trips!
see: e.g.
http://sanpark.co.za/parks/kruger/
Otherwise, this company has an excellent reputation.