I don't think you'll have much trouble filling those requirements.
You mention mountains but not the hunting elevation(s)... high altitiude (6,000' ASL and up I'd say) is a real bonus for LR shooting and hunting (if you're prepared and have the trajectory and wind data).
I've shot plenty of 24" barreled rifles to 600 yards...no problem. Remember, the bullet has no trouble getting to 600 yards (or even much further) it's the shooter that needs to understand and correct for trajectory and wind.
300 Magnum (traditional or short) would be a good pick. If the Short Magnums will fit in a short action you'll save a bit of weight. Left hand might be a problem in a Short Mag but you should be able to find a 300 Win Mag in left handed somewhere.
I'd definately have a bipod on that rifle (or one pack available to attach).
Long range does NOT require a heavy barrel (IMHO), it requires an accurate rifle and good marksman. You'll probably only need one shot once the critter is spotted and there's no need for a heavy barrel when shooting a one (or two) shot string.
Get good equipment... a few knocks and bangs on the rifle and scope should NEVER alter your zero...what good is a rifle system that can't be trusted to hold zero in the outdoors environment. Get a scope with target (or Mark 4 type) turrets or calibrated reticle (Horus, Mil, MOA)...stay away from the preset game type reticles (Shephard, Springfield Armory, etc).
I've had two custom HS Precision rifles (2000 LA), both were the heavy model. The 300 Win Mag was probably one of the best shooters I've ever had but the second one was a POS...I won't buy any more of their rifles!
You don't need custom rifles
to be good for 600 yards...custom rifles (IMHO once again) are great for confidence builders...You might go through a dozen factory rifles before getting one that's a keeper but a custom built by a trusted smith is a sure one-time deal.
I'd say get the Savage (can't believe I said that [img]images/icons/wink.gif[/img] ) and practice/evaluate. 600 yards is fairly close shooting once you have a good grasp of the basic ballistics and techniques.