I would go with the 7600 or the A-bolt, not necessarily because of the rifles, which I like, but the cartridges. I would be hard pressed to choose, but I have a 7mm Rem mag only because the left handed rifle I wanted was not offered in .280. Have used the 7mm Rem mag on both whitetail and Black Bear myself, and it was plenty of cartridge, in fact it proved a bit too much for deer at woods range.
If you had not mentioned elk, then the Stevens 200 in 7mm-08 would be an excellent choice for deer and black bear, IMO. It would work for elk, too, but for some reason, I would feel more comfortable with more powder behind my 175 grain bullet.
The .280 or 7mm Rem mag are both about the best all around cartridges out there (IMO the 30-06 and 270 beat them only because of ammo availability, otherwise they'll all do the job). Plus they have the edge on the 7mm-08 in that they can send a heavy bullet out there a little faster.