Rick,
I took the same trip last October! It was absolutely fantastic. I took my D3100 with a 18-55 and a 55-300 lens. The 55-300 was used 90% of the time but the 18-55 was nice for wide landscape shots and when the animals were right next to the truck (really, an elephant brushed the front bumper of the truck and a lion took a nap against a tire in Ngorongoro!). I took about 3000 shots. You can take a look here:
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The 55-300 worked great and was comfortable to carry. I saw some guys with 3' long, 500mm, F2 lenses - lugging that round was no vacation!
The best accessory I took was a monopod. I set it for about 24" and could steady the camera on the roof of the truck or even tuck it in my belt to steady the camera. Helped a lot and was easy to carry. A few times I wished I had a tripod but I had to balance that with lugging more gear around.
If you would like to talk further, feel free to write me at bdmann *at* gmail.com.
Brian