Absolutely Wes, this is a great suggestion for coming in early and doing something independently. Capetown is a city so there may have many great possibilities for coming in early and doing your own pre-trip and be pretty easy to get around.
In fact before or after the package anyone can and do many things independently. I am not an expert on Africa to know if this would be difficult or not if you are trying to do things such as Nambia or other camps.
The key thing is the ability to get from A to B, organize flights (particularly the charter flights)transfers and accommodations etc. Also not sure how safe it would be if just two people were running around independently. Capetown is supposed to be fine but Johannesburg is not a good place at all. You note we are flying in and flying out of Johannesburg only.
I know I would never consider doing things independently in Kenya. Nairobi was a scary city and there were no private transfers available around the game parks, everything was organized by safari outfitters.
Sometimes it is just easier to go with the complete package, organized by people like Ker and Downey who are experts in the area, sometimes you can do things independently. Everyone's choice.