I have used my .300 Wby in Botswana with splendid results. When it comes to the .300 magnums I don't see why anyone would look elsewhere, unless of course you like the classics and go for the .300 H&H. My one suggestion is that you load up some heavier bullets. I've used 220 loads on Eland and Kudu. That's one of the beautiful things about the Weatherby... it is a modified H&H and as such can comfortably shoot the heavier bullets.
Though I have not (yet) hunted Tanzania, Botswana has gotten so expensive that Tanzania or Namibia will likely be my next visit. Most of these countries allow 2 rifles and 1 shotgun, though if the Lawdog has gotten good advice that 3 rifles are acceptable in Tanzania then I'm sure they are.