When manufacturers machine the barrel channel on stocks they often use an undersize cutter, and a computer program these days to create the shape of the channel. You often get a well fitting outside contour that way, but because the cutter goes up one side of the channel, and down the other, it sometimes leaves a little ridge in the center of the bottom of the barrel channel that the barrel can rest on. When you fire one round it is on one side, and sometimes the vibration of the shot will move the barrel to the other side of the channel for the next shot. That is what creates that side to side shot dispersion on the target. Often rifles that have this problem will exhibit a telltale squeak if you move the barrel side to side in the channel physically. Usually, just a little light sanding with paper around a dowel or similar will remove the issue. Lighter weight barrels are more suseptable of course. Good luck with your problem.
