A lot of well meaning advice here, even if somewhat misguided at times. It seems to me, that all the realistic possibilities revolve around keeping your Dad's 30-'06, primarily, and eliminating redundancy, making substitutions with consideration of your shoulder. I stand by the advice I previously gave as being free of personal bias: Being more of a Winchester guy, I just recommended a Remington 700, a rifle I respect, but might never own. The point being to match your Father's rifle exactly, except for caliber and recoil. Then, if you find yourself in a hunt that jusifies the power of the 30-06, it will feel the same as your 243 that you usually use and practice with. I prefer a 270 over 30-'06, but only slightly, with all else being equal. In your case, the preference is your Dad's rifle. Since all other options revolve around that rifle as the only constant, eliminate the in-between calibers and go with a 243 Winchester, or, as I said before, a 6mm Remington, which should only be preferred if you are a reloader.
Next thing you know, somebody's likely to say, "You need to get a 45-70!".
Forget the 7mm08; any load here that comes close to a 270 Winchester will also recoil like a 270. It cannot be otherwise.
The 260 could be a good compromise, but you already have the 30-'06. Eliminate the compromise.
Remember,your gonna be a two-rifle-guy; not a one-rifle-guy.