Having been to Kruger a few times here are my 2c.
If I were to go again I would take my 200-400. Period. I would miss my 500 f4 for the birds, absolutely I would. If I were on a tight budget and needed to rent something, I would look at the 300 2.8 IS and TC's.
The thing people look at when adding a 2x to the 70-200 is how sharp it is. It is quite sharp at f8 and 400mm, but the other thing I want is nice Bokeh and the 2x TC option will not do that unless you are really close to your subject. Already you will often encounter bad Bokeh from sunlight and heat shimmer, the 2xTC option will make multiply that. With a 300 2.8 and TC you will be 50% closer to your subject than with the 70-200 and TC. Making the Bokeh cleaner. Also useful for those birds shots (often in camps and at places like Panic Lake will be useful).
I said above I would take the 200-400. The 500 for birds is great but the best shots are likely to be early morning or just before the gates close. My best sightings and shots came at these times and near the road I was on, often 400mm was too much, 500 was a head shot. 200-300 at f2.8 would work great in many of these situations. We can now pump up the ISO way more than I could last time I went with a 1Dmk3 and 5DII. 200-400 at f4 is perfect. Budget option of the 300 2.8 is my second choice only as it take TC's so well. Does mean you have to swap TC's around and dust could be a problem.
70-200 however is still useful for larger animals, quite often you will be close to elephants and realize how big they are
The rest. I would take a good wide angle, some nice landscapes in SA especially if you visit the Blyde River Area before Kruger.
Take two bodies. Longer lens on one. Shorter tele on the other. I did try to help a French guy in Kruger last I was there, his focus screen fell out when he tried to clean it (not a good idea anyway) but it broke and it was his only camera.
Kruger is a good start to African safari trips, actually cheap and easy, you also drive when you want and are not restricted by guides. Drive to the north, it is beautiful and less busy.
Forgot one more thing with long lenses. If you are needing 500mm to fill the frame with a big cat, rhino or buffalo then chances are your shots will be soft as hell with heat shimmer anyway. This king of thing only works early and late, mainly early (until 9-10am). The shots you get up to 300-400mm will be better than most above that). Exceptions being over water, hide at lake Panic or sunset damn are great examples, or dull days (even then it can be warm enough to distort images).