7 mag with a heavy bullet (180 VLD) is my choice. I've seen it work great at very long ranges enough to have full confidence in it. I don't like brakes and the need to place the bullet as precisely as possible makes the lighter recoil a huge benefit for longrange work. I'm a big guy and shoot enough to have a decent squeeze, but without a brake I can't shoot a 300 ultra, 338 , etc, well enough to shoot at those distances with confidence. I also found I just didn't want to put in the range time or field practice because they were unpleasant for me. Too many times getting ear protection on in the field doesn't happen and brakes are brutal on unprotected ears. I toyed with the 7 STW and it worked great but equally great results with a plain 7 mag left me with no reason to burn the extra powder or let the extra pounds of recoil that come with any bigger caliber affect my shooting.
Whatever your choice, knowing your rifle and being able to put hits where you want them will be more important than caliber choice. Finding the comfortable balance of energy and shootability varies a lot from one shooter to the next.
I'm probably in the minority on this issue, but bigger caliber does not mean better in my case. I'm a big fan of 6.5mm selections for elk as well although they need to be used within their limitations. A 264 Win mag or 6.5x284 applied correctly isn't out of place as a longer range elk round.