I have always liked the idea of a 9.3 x 62, in BLR. I'm not proclaiming it to be the only, or even the best rifle for what you are describing. It is just something that appeals to me.
The 9.3 has some serious hitting power, the recoil is manageable enough that you could fire it at a moderate rate if you had to.
I think you can still use a 9.3 x 62 in most parts of Africa, but I could be wrong.
I've never owned a BLR, but it has not been for lack of interest, just $$$.
However, if you changed the parameters to a "stopping rifle", I would not go with this combination.