Any of the calibers you named are perfectly adequate for deer from the end of the muzzle to 400 yards. All of them will do the job and I doubt that any of the deer you hit would ever know the difference.
So, you are really getting into gun looney territory. You don't need a new rifle, but if you just have to get one, just pick a caliber and go with it. All of those are adequate.
If I could only have one of those mentioned, I would go with the 30-06. It shoots heavier bullets marginally better than the .270 and the 7mm-08. It has less recoil and muzzle blast with only slightly less performance than the .300 mag. It is cheaper to shoot than any of the others and you will can find 30-06 ammo in a grocery store.
This post was edited on 12/6 at 10:03 am