They hang out across a steep nasty canyon. Theres no way to sneak into the side that they're on. Way too thick and nasty. What you can do is shoot across the canyon. Its a 970-1170 yard shot across to the hole they hang out in.
If it's way too thick and nasty, how do you propose to get there to retrieve the elk in the first place? Can you pack the meat out once you get there?
Have you ever shot across a canyon at all? Have you shot across a canyon that's 1,200 yards wide at all?
The wind at this yardage can be daunting to say the least. Lots of threads make a 1,200 yard shot sound like it's a chip shot. But the wind, acting squirrely on any given day, will wreak havoc on your 'chip shot'. You will need to know with a good deal of precision just how fast the wind is blowing and from what angle.
Can you see what the wind in that canyon is doing, in the interval the bullet has to cross it? That's what would give me pause to rethink the shot. Then you need to know with excellent precision just how far that shot is, hoping against hope you can make the shot before the elk moves, even a tiny bit.
If you have all the above nailed down pat, I suggest putting that 10" gong out at 1,200 yards in various situations and shoot until I could hit that gong every time. Along with this comes the practice of reading and measuring the wind. A knowledgeable spotter can be a real blessing.
I can tell you from experience, you need more energy and velocity than any 7mm can give you, yes, even that highly vaunted 7STW. The big .30 calibers are minimum and the .338 (think big!) is just about perfect. This is not a game of luck, this is real life and you need your t's crossed and i's dotted. Plan for everything, practice for everything.