Having worn out my share of barrels, I've never "broken in" any of them. They started out so - so, ok or tack driving for accuracy. Never changed over the life of the barrel to when test groups opened up 50% over what they did when new.
97%+ of all commercial factory rifles have their barrels somewhat sloppily fit to their receivers; not full and even contact all the way around. When they're fired, the metal gets hot and expands. As the barrel expands at the high/hard contact point around its fit to the receiver, a stress starts at that axis. The barrel bends its muzzle off the intended place and bullets start moving away in some direction from the point of aim or zero. This is the main reason factory rifles are guaranteed to some level with only a few shots; typically 3. They (ought to) know after a few shots are fired, the barrel will bend as it gets hot and start walking shot impact away from the point of aim.
All my four new factory sporter rifles did that shot stringing stuff as they heated up. Same thing with two factory Winchester "match" rifles. The people I know who bought Remington's 40X centerfire match rifles all reported the same thing. Few, if any, factory rifles have their receiver faces squared up with the threads barrels screw into.
Yours might be fixed if a gunsmith could take the barrel off, face the receiver square with the barrel thread axis, then shim the barrel so it clocks back in correctly for headspace and other parts to align properly. If it still walks shots after that, then the barrel is not stress relieved properly and bends on the stress axis as it heats up.
Or shoot no faster than once every 5 minutes.
Learn how your rifle walks shoots as the barrel heats up, then make a sight adjustment every shot or two until the barreled action stays hot and shots no longer walk around.