I have done a very similar safari - South Africa, Zambia, Botswana, Namibia, Victoria Falls. Without knowing the specifics of your itinerary, a lot of Kruger is boutique safari where the vehicle will get up very close to the animals and you won't need more than 300mm to get great shots and in a lot of instances you'll be grabbing for your 70-200 as the range can be inside of 10ft and having a zoom is almost a necessity. Birding is a different story. There are many fantastic birds throughout all of those locations and the more reach the better. For Chobe and Botswana, its wide open and you need quite a bit of reach. You'll want an extender on your 300mm pretty much all of the time if that is your longest lens. I don't recommend swapping lenses or extenders in the jeeps, it can get pretty dusty. I really think you will be more than happy with the 70-200 and probably a 1.4 on your 300. The 200-400 1.4 certainly gives you a lot more flexibility, but it is an added expense. If money is no object or you were starting from scratch, I'd say the 70-200 and 200-400 1.4x is a perfect combo. I really wouldn't worry about 2.8 on your long lens - by the time you're positioned on wildlife in the morning there will be plenty of light. You'll probably do 1 maybe 2 dusk safaris in Kruger where you'll want 2.8, but you'll have your 70-200. The flexibility of reach having the 200-400 1.4x far outweighs it being 4.0 if you decide to go in that direction. Weight of gear isn't an issue. You might do 1 or 2 walking safaris, but the animals freak out at human footsteps and get very skittish (whereas they aren't bothered by motor vehicles) it will likely be more of a vegetation nature walk. The rest of the time you'll be in the jeep and can have one camera in hand and one resting beside you. You might want a stabilization sack or a monopod for your white lens.
Bugspray, full brim hat, sunglasses, lightweight neutral colored clothes, hiking shoes.
You'll be happy to have the 24mm for sunrise/sunset/stars. 17-40 will be good for around camp and at the falls
Sounds like a trip of a lifetime. have a great time, and you'll be happy and have plenty of photographic opportunity no matter what decision you make on gear.