Nikon 80-400 or Sigma equivalent will be the perfect combination for Safari.
I would avoid the use of a converter, as the last thing you will want to be doing on the vehicle is fiddling with one. It will also increase the chances of dust on your sensor.
Make sure you get VR/OS as not all vehicles turn their engines off, so even if you are well braced, engine vibrations will still be there.
I don't use Nikon, but took a Canon 100-400 on safari, and it was excellent. Best compromise for range.