When barrels are made they have a natural "bend" in them. The bend is then corrected to make the barrel straight. When the barrel is heated up through repeated firing the barrel returns back to its natural bend or "happy spot". The barrel will always shift back to origional POI after it cools. If you use the barrel to fire a few rounds here and there it will be okay. If you use it for matches and fire strings of ammunition you will notice the shift.
This is what seperates "select" match barrels from the other match barrels. The selects are the straightest barrels that when checked for runout/straightness are within spec and do not need to be corrected. Thus the barrel is already in its "happy spot". Factory tubes are usually just mass produced and screwed on. You could talk to savage about the issue. Maybe they would be willing to swap out the tube if the 10 rounds they fire are able to produce the results your getting. Ask them what there procedure is for the 10 rounds. If its fire, wait 5 minutes, fire again then chances are you'll be SOL as they wont see anything wrong.
This is just my .02 cents on your issue. I have the same rifle as you and the factory tube would shift as well. Mine would move up and left.
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