You're trying to serve 2 masters and you will not enjoy the results of doing so. A hunting rifle is light and accurate and should be something you test fire from a cold bore. Waiting several minutes between shots with the bolt open and chamber empty so air can circulate is necessary and right for such a gun. If the barrel were heavy enough to sit around shooting it in long fire strings then you'd definitely not want to carry it in the field. Trust me on that. No matter how big a stud you think you are, a 8lbs rifle is appreciated a lot more 5 miles into a hunt than a 11lbs rifle.

For shooting from the bench at paper and steel you should have a different gun, something set up for that. Another savage 111 is a fine option but you'll want something with a nice long heavy barrel on it, something in a bull/varmint taper. I'd start with at least a 24" tube and really I'd recommend a 26-28" barrel of at least varmint taper if you're intent on staying with a magnum. If you want just good long shooting fun at the range, I'd pick up a Savage 10FP in .308. You can shoot that quite a number of times before it gets really hot.

Secondly on this front and this bit is PURE opinion: .300WM is a magnum calibre and will chew up barrels much faster than say a .308 would. If you're just popping paper at a couple hundred yards you don't really need to burn all that extra powder and soak up all that extra recoil and burn up barrels.