For South Africa, I'd consider Jannie Otto Safaris. Besides being around for about 30 years he has an interesting, slightly different package scheme.
Instead of a list of animals he sets up 3 lists and your package includes a couple or three animals off of each, which you can pick on the fly if you want. That gives you near infinite flexibility to change your mind or take advantage of unexpected opportunities, without entering into some kind of negotiations.
He also operates in 5 other countries, if you want to change things up the next time.