I think my dream mountain rifle for what you describe would be a:
Blaser K95 Ultimate Carbon
7x65R
Scope: Reticle allowing for wind-hold (Leupold TMOA, Swarovski 4W, etc), but still reasonable weight, with a dial-up elevation turret with zero stop and lock
Gun is just over 5 pounds plus scope and mount.
23.6" barrel, but the single shot design will be shorter than a bolt gun that has a 20"
Electronic ear plugs, much lighter than any suppressor
I see a lot of people repeating the "don't put a magnum in a short barrel". A lot of us tend to pick a cartridge we like that's in the neighborhood of appropriate for game we are hunting in general terms, then get to working out barrel length and the other details, but this isn't the optimal approach. Of course a 7mm Rem Mag in a 20" barrel vs 26" will have less performance, but a 7mm-08 in a 20" barrel will always be worse! For this application, efficiency is irrelevant IMO. I don't envision anyone shooting matches with this rifle. Barrel life, extra powder, ammo cost...why care? You aren't going to do enough mountain hunts in your lifetime to wear it out.
Decide on the largest target game. What caliber/bullet weight would be appropriate for that game. What's the longest reasonable shot distance, assuming optimal conditions. What minimum impact velocity does your bullet need (e.g. 2000 fps copper or 1800 fps lead-core). Work backwards using the b.c. of your bullet to determine required muzzle velocity. You could get to the same place with either a 16" 28 Nosler or a 28" 7mm-08 for an extreme example. If you have a desired barrel length, then you need to determine how much case capacity gets your bullet to the desired velocity out of that barrel (using GRT or Quickload)