Skin hit on the problem, thanks, Skin.
I trimmed some bedding material off the stock just ahead of the action this weekend and went to the range this morning. First 10 shots at 100 yards had moved 2" high and 2" right. So I decided to try a little experiment. I tore a sheet of paper from my pocket notebook, folded to to about 1/2" wide with eight thicknesses, loosened the action screws, put the shim in front of the action under the barrel, tightened the action screws, shot 20 rounds. All of them were 8" high, 8" right, and this was with 10 in-lbs torque on the action screws.
The barrel simply isn't tight in the action. Not loose enough to feel in hand, but loose enough to allow the barrel to move---relative to the action--about 11 moa. This is why the Savages are sensitive to action screw torque, those barrels which are on the small side of the tolerance OD, when combined with an action on the large side of the tolerance in ID result in enough clearance that the gun isn't reliable from shot to shot. If the scope was mounted on the barrel, it wouldn't be a problem. If the barrel was screwed in to the action and then jam nutted, it wouldn't be a problem. Perhaps with shim stock, JB-Weld, torch, freezer, and a big hammer, it won't be a problem. On second thought, I might talk to a real gunsmith first.
I'd be mad except now I understand why I see what I see, and that is progress. My old engineering mind is happy, actually.
This is fun.
Joe