Hi BriAn,
Re vehicle rental:
To my knowledge, the only decent 4x4 rentals in Zambia is Hemingways from Livingstone. They have fleet of well equipped Hiluxes, but their rental prices are on the high side. I have never rented from them, but they were always prompt in answering my iquiries. For our three trips to Zambia, we have always had our cars delivered to Lusaka from abroad - twice from SA and once from Namibia. I still always worked cheaper that way for us.
As for time of travel:
I believe November/December period will probably not work for you, at least not for the parks/areas you intend to visit. Busanga is inaccessible once the first rains arrive and all camps there close down at the beginning of November. I think you have zero chances to even reach the plains during mid November.
South Luangwa is accessible all year around and at least main roads in the park should be passable in November/December. But North Luangwa is different. When first serious rains arrive, the park becomes inaccessible and few camps/lodges that exist there, close down for almost half a year.
Re independent camping:
There is no independent camping possible in Busanga Plains. Accessing the plains even from the closest campside inside Kafue NP require a lot of driving, so day trips there are probably very exhausting and their merits are questionable. One of the lodges from Busanga did run a special offer for self drivers at the end of this season, so catching one of such offers is probably the best idea for self drivers currently.
There is also no campsites inside South Luangwa NP, but there are quite a few campsites available just outside the park along Luangwa river. We have stayed at Wildlife Camps and At Zikomo and both are excelent camps with lots of wildlife around and inside the camp.
In North Luangwa NP, there is again no camping for independent travelers. The closest (and most affordable, but still far from cheap) option to camping is using self catering option at Buffalo camp.
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