I don't think that a 30-06 is a long range elk gun, they have their place and work well but I think most folks around here would say that it runs out of steam a little too soon to suit them.
Both the 300WM and 7mm RM are good long range calibers for what you suggest but for my money, the 300WM kicks a little too much to enjoy an afternoon of shooting unless you're going to put a muzzle break on it and then if you're going to muzzle break it you should maybe consider a 338 because with a good muzzle break on it, one of the larger 338s can still be very comfortable to shoot.
Therefore, the outstanding advice of somebody about 2% as competent as the competent folks around here suggest a 7mmRM. The recoil isn't unpleasant, the high BC bullet selection is fantastic, I get 100 rounds to the pound, and the number of elk, bears, and deer that can vouch to it's effectiveness are ever-increasing.