Is a 7-08 with 140 grain bullets really that much different from a .308 with 150s?

Why not get a .308 sporter weight rifle and put a steel floor plate on it? 130 TTSX probably won’t kick much either. The Win 70 Super Grade in .308 Win might do it. 6.5 CM would be even less recoil but the barrel life might not be as good.