I bought a Weatherby Vanguard years ago in .308 that has been superb in the accuracy dept - actually, all "departments". Yet that desire for more power nagged at me for years. I kicked around a .300 Weatherby, .325 WSM, and .338 Federal, but just could never convince myself why I really needed another rifle/caliber combo. I've taken four elk and a black bear with this rifle (among other things), and, a couple years ago just decided I didn't want or need another. I stick to 180 bullets (even for varmits...to cheap to keep resighting.) as it seems to shoot them the best, even with the 1/12 twist.
.308 is fine for elk, and it's a lot cheaper to practice with it - even if you do reload, as bullets for the .338 are more expensive, less diverse, and a bit tougher to find, than the .308.
One of the guys I hunt with bought the Kimber 84M a few years ago and he's been quite happy with it. Good choice!