I would get the 7mm-08 and not look back. The cartridge would be almost perfect for such a gun for deer.
You already have a .30-06, so the .308 is not a significant difference. You have a 270 winchester, so while a .270WSM is significantly faster, such a cartridge needs, in my opinion, a longer barrel - like 24".
While you have a 7mm Rem Mag, it is a very fast 7mm cartridge. So while the 7mm-08 is significantly shorter and slower, it will be less affected by the shorter barrel. Plus, the 7mm-08 is really the ideal deer cartridge out to 250 yards - you really don't need anything bigger or faster.
Zachary