Sorry to hear about your house and lenses.
Having been on 3 safaris (4th one next year), one word applies. That word is "REACH". Out of the 2, I'd got for the 70-300. It's a lens I used for the 1st 2 safaris and got cracking shots, also it is lighter and has more reach. The best would be a 100-400, as even though it is heavier, the images are awesome and 400mm is a big step up from 300mm, if you can stretch to that. If you buy second hand then you can ususally re-sell it for £50+/- what you paid for it, effectively making it a "free" lens. My wife and I stepped up to the 100-400 for the last safari and it was totally worth it (and we made £50 when we sold it the week after the safari).
Yes, the 70-200 is good for low light, not as good as the Canon 2.8 IS II, but even so, you can only crop so far and believe me, the extra 100mm or 200mm is invaluable for catching those moments. You could go for the Tamron+doubler, but not too sure about focussing speed, and that makes it a 140-400 f5.6, making it good for long range, but further reducing the wider side of things.
Because there were 2 of us on the last safari, we had 2 bodies each and covered 10mm up to 400mm with the 10-22, 24-70, 70-200 and 100-400, but if it was just me, I'd be going for 70-300 or 100-400mm, and if yo ucan stretch to a cheap second body for wider angle stuff, it would be worth it.
Whatever you decide on, remember to take time to look with the naked eye and soak it all up. Whilst it's great to take the shots, it's awesome just to observe the wildlife and the sunsets
PS I would avoid the big Sigmas as they drop to f6.3 very quickly, and aren't of as good an image quality as the 100-400 (compared some shot on the last safari with some that had one and they were a tad gutted)