Put in for Mountain Goat and Bighorn Sheep tags and use it for them. I can't think of a better description of a 'mountain rifle' than such a cartridge in a nice compact full stock with a low magnification fixed or variable power scope on it mounted with quick-detach rings and iron sights as a back-up.
As far as elk are concerned, I would prefer something bigger. I'm not a 'magnumitis' case, I own no magnums. I've just seen elk take off and cover ground so fast, or put terrain and cover between you, as to be out of effective range before you could ever cycle the action and get off a well aimed second shot. If your best, most well aimed first shot didn't cut the mustard, and you can track and catch up to them, will you be able to pick out the same animal with confidence from a herd of thirty?