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.
The operator is a South African company called Kiboko Adventures which I would recommend unreservedly. They target an age range of 45 and up, although there were a couple of people on my tour who were younger. Most of us were in our 50s and this particular group were from Australia, USA, Canada and Spain with a Zimbabwean guide/driver.
The accommodation was advertised as 2 to 3 star but most exceeded this. For someone who normally backpacks and stays in dorms or now that I am older, in cheap hotels, it was quite different to what I am used to. Here are a few of my favourites.
Die Dorphuis in Calvinia, South Africa
Transkalahari Tented Camp in Kgalagadi Transfrontier Park on the border of South Africa and Botswana
Weltervrede Guest Farm outside Solitaire in Namibia
Okakuejo Rest Camp, Etosha National Park, Namibia - one of the best
Finally, my favourite of them all - Ngepi Camp on the Okavango River in Namibia's Caprivi strip.