I think you're going to be disappointed in the 300 wsm. It really doesn't make much difference in ability to kill an elk over your 7-08.
I'm thinking that we're I starting over, I'd likely choose a 6.8 Western (basically a fast twist 270 wsm) or a 300 PRC ( another fast twist short action magnum) as my big game / hunt everything rifle.
I live in and hunt North Idaho, been using the same rifle for elk since '88 I believe. The finish on the walnut is gone again, it's on its second Leopold. It's a .338 WM, but with modern bullets it's not necessary. It's familiar to me, and accurate. It is very effective though.
I have a few others I could choose, and truthfully most stay home. I hunt when it's deer and vermin season, with a 257 Roberts, 223, or often a 25-06 if I'm going where long shots are possible.
When it's Elk season it's usually the old reliable, but I've honestly seen elk just as dead with a good quarter bore bullet in the boiler room.
Bullet choice matters way more than the delivery system, if equally accurate. Pick a bullet that performs the best for the way you use them , not what all the experts on the internet tell you to choose. Monos aren't my favorite for anything I use currently.
With a fast twist barrel in one of these two choices you won't be limited by your firearm at all. You would have much broader availability in choices for weight and construction. Every manufacturer has several choices in .308"!