I voted 8mm Rem Mag out of the options you listed. Nearly obsolete, but for no good reason. It has performance that bests the .300 WM, hits as hard as it's (kinda) parent .375 H&H, but with a better trajectory and more retained energy down range. I never understood why this cartridge failed commercially. It has fantastic performance that is hard to beat for an all-around cartridge to hunt things with large mass and/or sharp claws and teeth. People who own and shoot it wouldn't trade it for anything.
.375 H&H would be my second choice, followed by .300 Win Mag.
Personally, I opted for a Remington 700 BDL SS in .375 Ultra to handle my future Alaskan and African hunting. Trajectory of a .270 with energy that rivals the .458 WM. Only thing is, in that light rifle, and with no brake, it kills on one end and cripples on the other. My first time out, my hand crept up on the grip too far, and the knurling on the bolt ripped a good chunk of flesh from my trigger finger. Never got scope-eyed, but have felt the rain guard tap my brow.
This is the unit, topped with a Leupold VX-II 4-12x 40mm. My loads are a the "light" one, which is a 250 gr. Sierra Gameking at 3,110 FPS for 5,370 FPE and the sledgehammer, a 300 gr. Gameking at 2,970 FPS for 5,877 FPE
