The best way to cover this route is to hire your own 4WD and take your time but if, like me, you don't drive, have limited time and hate camping, this trip or something similar is a good compromise. It was in an overland truck, as they all are (except for the most expensive) but accommodated rather than the usual camping.
I was away for 6 weeks in total with the first spent in Cape Town and the last two with a friend in Nairobi. The tour part of my travels was the Transkalahari, a three week overlander from Cape Town to Johannesburg through north west South Africa, Namibia, the Zambian side of Victoria Falls, Chobe in Botswana and a very quick sprint back to Johannesburg. The itinerary now being offered has been changed to finish in Livingstone and allow extra time elsewhere.