I have never shot the model 111 LRH. However, I'd imagine it would make a fine .300 WM rifle. IIRC, the weight is close to 9lbs. Add mounts and a scope and you're close to 10.5lbs. IMO, that's a good weight for a .300 WM.
Personally, I'd forego the .300 WM if you're only shooting 300 or 400 yards. A simple .308 or 30-06 can shoot 300 to 400 yards with enough energy to kill an elk.
If you do decide on the model 111 LRH in .300 WM, I suggest replacing the muzzle brake with something like the APA Little Bastard. I think an aftermarket muzzle brake will control the recoil better than the factory muzzle brake.
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