Arms move the hands in a direction. The barrels path follows. Barrel “lag” doesn’t happen backwards. It happens as a result of a loading barrel FROM the direction the arms take the hands in AND the weight of the bat.
Hitters shouldn’t force the barrel into centrifugal motion (left) at the start of the swing forward they should be working to produce a centripetal barrel (right) that will result into centrifugal motion. In other words swing the arms not the barrel.