Thank god you came to your senses by the end of your own post
. That 375 cartridge will do anything that you could ever want for the animals you listed. Best of all it is built around a standard length action, controlled round feeding, accurate, all weather rifle.
My 375 Alaskan is my primary hunting rifle (my moose season starts in 34 days), I also have one in 416 and have used it on everything from tree squirrels and bunny rabbits to cape buffalo but the recoil is pretty stiff and its trajectory really starts to suffer past 200yds.
Bottom line is, shot placement will determine the outcome every time!
P.S. "if I'm not satisfied with how 375 can perform, it's a ME problem, platform issue, or I should go all the way up to a 458." The .458 is only halfway there, .577 nitro (3inch, 750gr) or .600 nitro is all the way.