I've read accounts by professional hunters who always used .375 H&H rifles. The pros considered rifles like the big .600 Nitro Express and Jefferies custom double rifles to be fine examples of conspicous consumption by British noblemen with more money than sense. With a .375 H&H the pros could kill anything in Africa, and not give themselves a concussion from the recoil.

As for the shotgunners, I think that the largest gauge shotgun fired from the shoulder was an 8-gauge. Big monster market guns were mounted on some kind of pedestal and swivel arrangement.