I have done 2 safaris, first time in Tanzania and Keynia, second time Botswana. I had the 500f4 II on my 1DX and the 70-200f2.8 II on my 5D3. I find that the1.4x works well with both combo, but for fast actions at close range, taking off the 1.4x improves focusing a lot. I found myself constantly taking the 1.4X on and off one camera after another. I didn't take any shots at f2.8.
So to name the long story short, I think there is way too much overlap between the 70-200 and the 300. If you can afford it, the 200-400 is the way to go for mammals. If you are interested in birds, perhaps the 500f4 or 600f4 would be a better choice. Most of the time you will be on a safari vehicle, so a good beanbag will save you. Weight is only an issue to get there and in transit. Usually there is weight restrictions, but unless you abuse the rules, you should have no problems with say 10 lbs over.