Have you tried having the mod 7 fitted with a limbsaver recoil pad? (or other good pad) 308, 7mm/08, and 243 all use the same case, so using lighter bullets is probably the only thing that will make a difference in the felt recoil. My guess is that a 139 grain 7mm and a 140 grain .308 would be basically the same.
I think the recoil pad would be the most cost effective fix, and there are always the mercury filled tubes that most say work well. Probably a lot cheaper than a rebarrel. The .308 is not known as a hard kicker, but on a light compact rifle like my wifes Ruger 77 ultra light in .243, she could feel it........I had a limbsaver installed for her, and she's back in love with the rifle.
I agree with Peepaw, I'd look for another rifle and sell that one if I couldn't get the felt recoil down where I wanted it.