A couple of additional notes.
1. Several folks have mentioned dust and I too would recommend either a plastic sleeve for a long lens or at least a towel or something to cover your lens and body while the vehicles are moving and you may be in the second vehicle and hence in the dust trail. I think B & H has a plastic sleeve with elastic ties at one or both ends that would be very useful. (On my April trip to Tanzania we were at the end of the rainy season and the dust was minimal, but I could see that in dry months, it would be very dusty)

2. I frequently had my camera set to single shot priority but when we were anticipating action I would switch to high continuous capture. In a couple of seconds, it is then easy to have 30-40 or more images, so that contributed to the total number of images. I also found that with handholding shots, using back button focus was extremely helpful to get focus and then be able to reframe a shot as needed. and...

3. Don't forget to take some video clips...you'll get plenty of still shots, but sometimes a 30 second video clip is wonderful to show folks back home. This was great when we watched two female lions with seven cubs, some baby baboons on an old brushy tree, and some young elephants, etc.

Having just returned from South Africa - Kruger National Park - I can say that you definitely need the longest reach you have - the Tamron 18-400. Ask the tour people to provide a bean bag - I used mine a lot with that lens. There will be shots for which you wish you had an even longer lens. I used my Tamron 18-400 on a Canon 90D. You will also need a second body and lens. Take your 6D full frame and the 24-105mm lens. I found those two combos worked well for me. You can see some posts on this blog showing some of the shots I made. I'm absolutely sure you will love your safari!

I do some humanitarian work in Africa, so I have been on a few safari’s. I have recently used Nikon full frames and have yet to feel cheated by having only my 200-500 on one body and an 70-200 on the other in regards to focal distance. Beyond the 500 range, my images are usually disrupted by heat and haze that post processing only partly remedies. Usually at long distances, I now put down the camera and simply enjoy and marvel at the beauty. However, in regards to quickly capturing close up images, I have longed for a smaller, lighter camera as my second body. Several times animals have come up next to my vehicle and it was unwieldy to grab the second body then swing the big camera and lens into action (a FF with a 70-200 is large). My next trip will be with a micro 4/3 as my second body with either a 12-60, 12-35 or 35-100 lens mounted.

I can see the wisdom of having a smaller bridge camera and I think the advice above is sound. Several times now, lions and elephants have been too close for the 200-500, but those opportunities only last seconds. I’m not strong enough anymore to carry two FF cameras and remain rock stable and comfortable for long. But a FF and a Mirrorless 4/3 is still doable for when the shooting gets hot.

I usually tell first timers not to get so caught up with creating images that you don’t take some time just to enjoy the magnificence. Also, if you have a pair of high quality binocs, take them. If you don’t, borrow a decent pair from a friend who is a serious hunter. Your guide will see more with your nice binoculars then with his cheap ones. When he sees more, you see more. Lastly, take a small power strip that is for 240 V, not 110 (Amazon). You are usually on a generator and a lot of rooms only have a single plug. You’ll need the extra outlets for charging everything because power goes off after 11 or 12 in some camps. Saves stress. Enjoy, have fun.

When I went I used a 150-500 and an 18-270 on two crop bodies. I never changed lenses in the field. I also took a 50mm f.//1.8 and used it for 4 shots on a night excursion (which images turned not to be great) and a 10-20mm WA which I never used. The only time I changed lenses was in my room and that was only for the night excursion. Next time, two bodies a big tele zoom and a normal-to-moderate tele zoom will be all I'll take. Lessons learned. Have a great trip. I think from your list I would take the 70-200 and the 100-400. The Rangers get you very close to the animals.