RE: Weight vs. Power
Considering you're already in trim condition, and assumming you can't trim your gear any more than you have...I guess you'll have to deal with whatever recoil will result from trimming your choice of 30-06 and/or 7mm Mag to a lighter than usual configuration. If you insist on going to a "featherweight" rifle then you may want to tinvest in butt pads and or shoulder-pads to assist in the recoil taming that might be needed if you go super light on the rifle.
Since you're in great condition though....carrying an average weight rifle should just be considered simple exercise.