Aron, I bought a 300 RUM because I couldn't find a 338 RUM. I have a HUGE Nightforce scope, Badger 6-screw rings and base on it and it weighs a ton. I call it the snot-ejector. I recoils very hard. I was going to rebarrel it to 338 RUM but never did. I agree, ammo is an issue as with recoil but I would think you could adapt.
That said, I am thinking if you go to Alaska or Canada or big bear country you will want a round larger than .30 caliber. One of the first posts mentioned a Savage with a short barrel. That has my vote and I want one in 338 Win. Mag. Short, powerful and that caliber is the standard in AK, from what I am told, everyone on the street corner has a 338 round in their pocket. Find the recipe for ammo that it shoots perfectly with some premium or Berger bullets and have a custom BDC turret made by Leupold or Kenton Industries for a small 3-9x40mm scope and you can kill anything from chipmunks to polar bears.