Until you free float the barrel and glass bed the action you are going to chase yourself silly trying to get this solved. You must eliminate bedding as the cause then proceed to other possibilities.

Savages typically shoot well right out of the box but this is the best way to find the problem. You might also try a totally different scope that is proven to shoot good groups on another rifle. It' s the only way I know of to tell if the scope' s reticules are moving on you.