I would check the barrel and action seating to make sure it is still secure and floated properly, then scope the throat and barrel. Next, I would check the crown on the barrel.
The crown sounds crazy but I have a 7 Rem Mag that is just like your 06, had it 30 years before it started doing the same thing. I checked everything, all good. I was talking to a old school gunsmith who told me to take ultra fine Emory cloth and wrap it around a muzzle loader round ball and polish the crown with.
Not sure why or how but, the rifle went back to stacking holes on target again.
It's worth a try before going to a rebarrel job. It's still my favorite shooter.
Good Luck.