I do around 4 Safari trips a year to different parts of Africa, each trip anywhere between 2 weeks and as long as 6 weeks, 2013 I've spent 3 months on Safari in Africa.
If you intend/need to do a reasonable amount of Travel to get to where you intend to use the gear, consider your carry on baggage and what restrictions are going to apply, as Photographers we tend to think like Gun People, what gear always at the top of the list, the rest we feel we can take care of.
In Africa most Airlines strictly apply 8Kgs as a bench mark for carry on, I Fly Business Class where ever I can & that allows 11Kgs, on Main Airlines you won't be able to book an empty seat, but I do that on the small Charter flights between airports & the Camps, that allows me to carry more than the 20Kgs the smaller flights will restrict you to. Never ever ever ever etc, Check in Camera gear within Africa, it's a huge Business in stolen Camera gear in this Continent, won't make any difference who you Fly with, all the African airlines have the same issue, they simply cannot control theft from checked in Baggage, it's a total lottery.
Which brings me to Insurance, complete must if Travelling in Africa, don't leave home without it. Now Lenses.
The 300f/2.8 L II goes where ever I go, always. This is the absolute fastest focussing & sharpest Lens Canon make in my experience, works absolutely well with the III Series 1.4x Converter, pretty good with the 2x. But, you need to be able to get close, in most South African situations it's the perfect Lens, generally a lot of bush, Animals are generally closer due to the amount of bush. Completely hand holdable and I almost never use it on a Tripod or Monopod.
The 400f/2.8 L II is another superb Lens, I recently sold mine, but I've been extremely Happy with this Lens both in it's series 1 form and later when i upgraded to the series 2 version. But, it's still heavy, so expect to be using it for your best shots on a tripod or a monopod. I used to always carry as standard kit the 300 + 400 and 1.4x converter. 1.4x works amazingly well on this Lens, the 2x a little soft.
600f/4 L II, superb, just a brilliant lens, lovely weight, best shots again from a Tripod or monopod, crisp & sharp. 1.4x works just amazingly well on this Lens, the 2x a little soft. I use this Lens only when I'm scheduling to Safari in the Serengeti (Tanzania) or the Masai Mara (Kenya), the Lens needs large open spaces to be worth carrying, but if you have the open areas with Wildlife further away, this is the lens to have.
As soon as the 200-400f/4 was released I was about the first in Asia (Singapore) to get one, haven't for a moment regretted getting it, just a brilliant lens. Being able to to zoom to fill the frame 200-560 f/4 to f/5.6, my Imaging has taken a leap forward, way less cropping to get the right shot, close enough at 560 f/5.6 to be just about perfect. Light enough to hand hold for short periods, but gets heavy quick, used mostly again on Tripod/Monopod or bean bag. But, you give up light, it doesn't sound like a lot, but going from the 300/400 f/2.8 Lenses to a f/4 has required an adjustment, mostly now I shoot at minimum ISO400 as a Base where I may have shot a lot with the 300/400 at ISO200 as a base, but I feel the adjustment has been worthwhile. Major added advantage with this Lens is you don't need to change out converters, it's a flip of the switch in/out, that simple, huge benefit in lost shots, dust on the sensor etc, when I use the 600 + 1.4x I generally set the Lens like that onto a 1Dx Body and that's how it stays, I'de love to see a 600 with the Converter assembly of the 200-400f/4.
My standard rig now is 300f/2.8 + 200-400f/4 for places like Botswana, South Africa, Zambia, Namibia. If the Serengeti or Masai Mara it's those + the 600 and generally a hassle with Airline Carry On rules, which I either circumvent with bringing my son/s, extra seats where possible, pay off the check in person for a tag to allow the extra carry on.
All of these Lenses work exceptionally well with the 5DMK III or the 1 Dx, but, you will miss the 12 fps of the 1 Dx on Safari, nothing quite like it, the 5DMK III at 6 fps is Ok, but (there's always a but) it can't compete with the 1Dx, for Safari, the 1Dx is the Safari tool with spades.
I hope this helps, what ever you decide you can't go wrong with any of these Lenses, enjoy your Imaging.