I live and hunt in N. Idaho also and a few of my buds have .338s. It's more than needed for elk, but what the hey? One great thing about the round - here in the heavy timber and brush of the Panhandle it's sometimes a good thing to knock the animal down NOW. Sometimes elk run 50-100 yards (or further) after being shot and 50-100 yards in this kind of brush can be a long way when you're trying to track down an elk. They can disappear into the thickest stuff without a sound. Sure you can follow the blood, but sometimes they head for stuff that you need a machete to get through. A shoulder shot with a .338 using a GOOD 250gr bullet is a pretty good bet for knocking one of those big critters down NOW. Meat damage? Yeah, but three quarters is better than no quarters.
Personally I shoot a 30-40AI and have had no problems, but there is nothing wrong with a little more oomph. Recoil in the .338 is pretty stiff, but just put padding on your shoulder when sighting in at the bench. When you shoot an elk or deer you won't feel the kick at all. As far as deer, just hit 'em behind the shoulder. There will be no more damage than with any other round - maybe less than a really high velocity small bore number like a .243 or a 7mm Mag. IMO a .338 Mag is a great hunting round for these parts.