I've been in the Serengeti twice and neither time had any problem with dust, but I wasn't there during the dry season. The last trip I shot mainly with a 300 f2.8IS and a 1.4X on a Canon 1DIV (1.3 crop). It was way too long for some things (e.g., lions lazing next to the vehicle or the cheetah that climbed on the hood) and definitely too short for other things (e.g., most birds, leopards in the trees). To me, two bodies (e.g., a 70-200 on one and a 500 on the other) would have been very nice. And don't forget that sunrises and sunsets can be spectacular.
If you want some unsolicited advice, it is to pick your tour company carefully--make sure the guides are knowledgable, and the company caters to the type of trip you're interested in having and the clients you're interested in being cooped up with all day long.
My 2cents, I live in Namibia. I use a D3 and before that a D2xs. I use a 300mm F2.8 and a 500 f4. I have and occasionally use a 1.4x converter. What support you need is dependent to a certain extent on what vehicles you are going to be in. But what we do here is go to the bank and get money bags+/- 12 x 8, double them up put a zipper in them and travel empty. Then when we get where were going buy a bag of rice and fill it up, when we leave give the rice to staff. It will be appreciated. Bean bags are a must, I would also consider a monopod for the open air landcrusier game drive vehicles, it is a bit more flexible then relying on rail placement in the vehcile. INMO a 200 400 is too much weight and not enough length. I think the key goal in most wildlife images is sharpness which I do not think you will get out of a 1.7x converter. If I had to pick two lenses for a trip here, it would be my 300 f2.8 and my 28mm. I would give the really long shots up for fast in close.
The 200-400 is your best one-lens compromise, but one long prime (+/- converter) and another mid-range zoom (70-300s are cheap and good) on a second body gets you reach, flexibility, and the all-important backup body.
Changing lenses isn't that big a deal. Take a couple of pillowcases to cover the gear as you ride, and only change when the dust settles. Just be sensible.
Of course you're taking two forms of backup, with no single point of failure? Good.
I'm lucky to have been on safari twice (Zambia, Namibia, and Botswana). First time ('06) I took D200, 80-200/2.8 AFS, and 80-400 (bought for the trip, sold after), plus a D70 + 18-70 for scenics and backup.
80-400 quality is OK, but I hated the handling - felt like I had to fight it in a way I never did with the similar-sized 80-200. Maybe a third-party tripod collar is the way to go here (I used it on a monopod). I also hated being stuck at f/8. Much of your shooting is near sunrise and sunset, so the light is not so bright.
For the second round ('12) I took the D200 and 80-200 again, with 400/3.5 AI + TC-14b for reach (I go way back with MF), plus D90 backup/second and Canon s90 for scenics. Husband used his D90 and 70-300 VR. All 3 SLRs use the same battery, and no new body to learn. In poor light, I used D90 + 400 and gave husband the 80-200; both are dead sharp wide open. When the sun came up, we'd switch things around.
Inevitably, I'd have the converter on or off at just the wrong times, but I don't feel like I missed any shots - just not always ideal. Husband's zoom made up for my lack of flexibility with the prime, plus I could always grab the 80-200 on the seat next to me.
