All the ones you listed are good medium range rifles. You are talking serious long range and these are not what you want to spend your money on. To many better choices if you have the money. Without going to the chey-tac case you have three choices. Improved 378 wby case, improved full length Rigby case and excalibur case. If I am shooting serious beyond 1000 yards I don't even consider the ultramag or Lapua cases. I don't like to limit myself when it is just as easy to shoot a big gun off one of the cases I mentioned and get the critical extra 200-300 fps or so. Everytime you turn a click there is a fractional margin of error involved. You always want to turn the minimal clicks for windage and elevation. Therefore get a rifle that serves your purpose having to turn the fewest clicks for windage and elevation.
Two primary factors of error involved here. Your error in the input and the fractional error in the click adjustment. Your input involves the exact range to target, atmospheric conditions, angle to target, windage, etc. Every click you turn considering one of these unknowns is a factor of error. The more you can reduce your time of flight to target the more error estimation you take out of the equation. More fps equals less time of flight to target. This equals big gun, all are accurate so don't let some dummy tell you, oh but this one is not as accurate as that one, or this brass shoots way better than that. These are hints the guy your talking to doesn't have the experience needed to do the job you want. Your talking a long way out there and that requires considerable experience. I have shot all kinds of cartridges, brass and rifles for many years and made great shots with all of them. The rifle and the shooter behind it are the key.
If you are building a hunting weight rifle do one of the cases I mentioned for serious long range work. If weight is not a factor then do the chey-tac improved and consider the 375 caliber in that one for extreme long range. At the extreme long range your talking about you not only have gone well beyond the cartridges you mentioned but getting to the limits of the 338 caliber and may want to consider the 375 to do a better job at extreme distances. Again, it's not that the cartridge or caliber may not do it, there are just better ones as the range extends. When I lived in Colorado years ago we had a great range where you could shoot targets over two miles. With my big 338's I could get to 1 1/2 miles, but when I used the 50 BMG improved I could do it much better. I took a manikin out of a jeep at 1 1/2 miles with the 50 bmg imp and I could not do that nearly as effectively with a big 338.
I have built and shot long range hunting rifles for many years and you learn not to get caught up in fads or what's hot now. You look at the exact performance of a particular cartridge and if it is the best for your intended use. The best doesn't cost any more than the average. Remember when the range gets long, the fewest clicks, the less margin of error.
This is the long range hunting forum. My comments are considering that fact. I have taken many trophy class animals at long range for many years. It wasn't luck. Everything I do is very calculated. I remove every margin of error I can with everything I do while in the field. With my rifle it will shoot the bullet I want at the highest velocity accurately attainable to give me the absolute best opportunity to harvest that once in a lifetime trophy when I get that fleeting chance in field conditions. I bring home trophies, many people talk about the one that got away.
Think about what I have said and then start searching for rifles. It comes from a lot of experience.