I tried not to be TOO critical, holier than thou, understand everything you're saying about people from other areas of the country. If you like to shoot long range, fine. If you're skilled, great! I ain't tellin' ya how to hunt, just tellin' ya I don't know that much bein' I don't shoot over 400 yards. Someone said a 7STW ain't any better than a .308, well, okay, whatever. I'm not the expert, just that the numbers would seem to ME to give it quite a bit less drop out there at 600 plus. I've not run the numbers, though, and am too lazy to mess with it over a thread, LOL! But, for a guy that shoots 400 max, a 350 yard PBR is better than a 275 yard PBR. It means no hold over at all to my personal limit. I do have my drop tables taped to the scope to 500 yards for the .308, but around here that's not necessary.
Heck, for those coues, a .22-250 might be a good choice, or a .220 swift.
It sure don't take a .300 mag to kill one. I'd STILL think 7 STW or maybe a .257 Weatherby or something, but I like 7mm bullet BCs. Also, if you handload, .264 Win Mag might be just the thing! I just don't care much for .300 mag, not very good BCs and excessive recoil. Long range shooting, lighter the recoil the better for ME. Of course, some guys just aren't affected as much by recoil and it hunting situations it don't bother me much, but at 600 yards, even a LITTLE flinch would put me off. I can shoot the 7 mag fine, though and an STW would be about as bad as a .300 mag, probably.
Just tossing out some ideas. Hope I didn't come across as thinking I knew anything, LOL! I don't have a rifle, more importantly a scope, set up for that sort of shooting. If I got into it, I'd want range compensation, maybe mil dot or some sort of drop compensating scope. having proper glass for such shots is pretty important and having a gun that can shoot 1/2 MOA or better would be nice. My stuff, 3/4 MOA is about as good as it gets. A 1 MOA gun gets you 6" at 600 yards, not that good for coues deer, ROFL! Might as well be trying to hit a jack rabbit.
Appologise if I came off snooty.