If I was putting together a back country elk rifle then this is probably what I would do. First off you will probably be hunting in the thick stuff, or the scrub oaks, or the open timber. However a 200 to 300 yard shot would probably be tops.
So it sounds like you are packing in.
I would go with a TC Encore with a SS frame and a SS barrel from MGM. I would go with a 20" barrel in one of the 338 or 375 calibers. A 375 H&H would be a real dandy with a 300 grain bullet. But the 338 Winchester would also be great. I would have MGM put a 2 to 3 inch muzzle brake on the barrel making the overall length less than24 inches. This should tame the recoil a good bit.
then I would add a TH stock to the rifle. The TH stock will give additional ability to handle the recoil.
I would probably top it off with a straight 4X or 6X West German Zeiss one inch scope. With Picatinny rings to allow easy on and off for packing in and out.
This would make a great, lightweight, fast handling, short rifle to carry while hunting and shooting. And you would also be able to break it down into its components and pack the rifle securely and safely in your back pack when carrying in and out of the mountains. Tom.