I would go with the 7mm mag. The .308 has a rainbow trajectory, although is very accurate.
The 7mm mag has less recoil than the 300 Rem ultra mag, but still delivers impressive energy and is a flat shooter. The 7mm mag would work well for deer at long distance.
As for long distance shooting of big game it’s a risky deal. The animal could move as the bullet is on the way and you could cripple it. I have seen this too many times. However I have also seen one shot kills on deer and antelope over 600 yards. The animal must be still, the wind light or none, no rain and you have to be a crack shot. Some kind of rest is needed for a steady shot and boat tail bullets are a must. I strongly suggest getting closer than 500 yards, 400 yards would be a hell of a lot better. And forget taking a head shot. I was hunting in an area that all the locals bragged about taking 400 to 500 yards head shots. My hunting companions and I saw 3 deer in a few days that had part of their jaw blow off wandering around sick and starving, proof of those braggarts stupidity!