Not sure how much more accuracy you are expecting to wring out of that factory Savage tube, but I reckon there ain't much left...
Despite all the internet hooplah to the contrary, it's just not realistic to expect custom barrel performance from a factory barrel...
Custom barrel makers like Broughton, Bartlein, Kreiger, Hart, Lilja, Pac Nor, Rock Creek, Shilen, etc, are in business for a reason. If factory tubes delivered consistent sub moa performance, custom barrel makers would cease to exist...