The 375 H&H is an excellent cartridge and, in my opinion, an excellent choice for plains game. That's what I've used pushing 300 grain Swift A Frames . Yes, blue wildebeests are tough but so are the zebras. The 375 H&H will do it all without the violent recoil of the faster cartridges. The "kick" is more of a push.
Good luck on your safari!
T.S.