Dave - One other thing I just realized. You siad it is the model 11. Is it the synthetic stock? I've noticed on mine that (synthetic stock) if you rest the rifle too far forward on the stock (closer to the forend tip) it will tend to shoot a bit erratic. That's my only complaint about the Savage - their synthetic stocks are too flimsy. They have a tendancy to flex and could be causing differernt pressure points on the barrel changing the harmonics.
I keep my bags back at least to the center of the checkering and this eliminates the problem.