I have just spent two weeks in a safari vehicle, with three others, using the 600/4L IS II (with and without extenders) and the 200-400/4L IS 1.4x, on two bodies. Because of the dust situation, there is no option to drop the hoods and since you are not allowed to leave the vehicle in these parks, getting these monster lenses up and down through the open roof, or out through the small windows of the vehicle is anything but fun.
Swapping the current 600 with a DO version, provided my weight and size expectations are about correct, would be an easy decision. My wife used the 100-400 f4.5-5.6L IS II on a 7DII on the same trip and produced stunning shots. A tempting combo for a safari trip would be a 600 DO, with extenders and the 100-400, plus a 24-70.