Sounds like you've got it covered, WC264.
I've taken my 375 to Africa twice, and collected every head of game I wanted there with it, from hyena to Cape buff. I wouldn't hesitate to use it on one or more of the Tiny Ten, for that matter; Craig Boddington, among others, has used a 375 with solids for these little trophies.
There is no such thing as being "overgunned" in Africa, in my opinion. Yes, I may be hunting impala, but lion may be hunting me.