I don't know how much I can add to the discussion. I think you just have to make up your mind what you like better. A mountain rifle probably has a SHORT sporter barrel. Your .300 Winchester Magnum might not perform as well out of a short barrel -- not delivering the muzzle velocity and trajectory flatness it is famed for. On the other hand, you mention a "long range rifle" and mention a "bull barrel." That kind of rifle is likely to be heavy. There is a middle ground -- a normal sporter rifle, such as the Remington 700 BDL or Winchester Model 70 standard grade. I would think this middle kind of rifle would deliver the reputed performance of the .300 Winchester magnum without being too heavy to carry in the field.
By the way. I hunt with a Springfield .30-06 my father made. It has a solid walnut stock -- probably thicker than factory made stocks -- and a longer length of pull (15.5 inches versus 13.5 inches as customary in factory rifles). It is relatively heavy -- probably about 11 LBS with scope. I hunt at 11,500 feet and may hike in as much as 3 miles to hunt, and then hike back out 3 miles. Yes, it is a heavy rifle, but a standard weight rifle isn't going to be a negligible weight either. And this pales by comparison anyway when you start packing out elk meat on your back. People will agonize over 1/2 pound or a pound of weight during hunting . . . and then pack out 60 LBS of meat. Is a pound of weight in a rifle that big a deal?