Hi WARPhEAGLE,
What a Post!!
First off youre coming up here from Alabama. Thats not going to be easy, the air is thin up here. Youre going to be sucking air like crazy no matter how good of shape youre in (the locals have a hard enough time in the mountains). Pick your equipment wisely and that means everything including your clothing. You need light equipment.
As far as a rifle goes, any caliber rifle that shoots at a minimum, a quality 150 grain bullet traveling at lease 2600 fps (accurately) will kill an elk to 200 yards. Anything heavier and faster is gravy and anything lighter is marginal, if not a stunt.
The 3 calibers you mention, 300 Win, Wby, Wsm are good calibers. All 3 will thump you (particularly the Weatherby). Can you handle the thumping? By that I mean, can you shoot it without flinching?
No matter how big your bullet is, the speed its traveling, or distance it has to cross. If you dont place your bullet in the Vitals of an elk (a hard hip, spin, or brain shot will stop them but thats not were I usually put my crosshairs) its going to be traveling some distance and its not always to an access road.
Its your money. Buy anything you want as far as a rifle goes. But all you really need is a 270 Win. That you can shoot close to MOA with a 150 grain bullet.
I personally like the 7mm Rem Mag, and the 300 Win Mag for elk. But Im not afraid of using a 270 Win, 7mm Mauser, 308 Win, or a 30-06.