Last month, I had a client ask about a June trip with the exact same budget as you. After lots of consult, we decided on one night at the Intercontinental OR Tambo, four nights at Tintswalo (private reserve adjacent to the Kruger) and four nights at Tswalu (million acre private reserve in the Kalahari portion of South Africa. The two lodges have similar names but are not related. The trip ends in Cape Town with four nights at the Cape Grace. On safari, the clients are using a private vehicle so they do not share the land rovers with other guests. Including all flights and transfers, this entire trip was 119,687 Rand per person or $7,923 per person at the exchange rate in effect in mid-December. This type of luxury trip would certainly work with you budget range and you could substitute one of the other lodges mentioned above for Tintswalo if you wanted. You could also sub Vic Falls for Cape Town. My favorite properties there are Victoria Falls River Lodge and Elephant Camp.
Anyway, there are a million options. My point is that your budget is quite healthy and will get you a good trip for 10-12 days!
Good luck!
Craig Beal - owner - Travel Beyond