The concept of the parallel "stabilizing" the shot doesn't make sense to me. The shot, seems to me, must be getting its sideways velocity after muzzle exit; there is very little room for sideways shot movement while within the confines of the barrels walls. The shot pellets are given a sideways push by springing off one another when there is suddenly no push from behind and no barrel wall to confine them such that they can relieve the pressure within the column. Also, the entrained air will expand and add a sideways "wind" to the muzzle exit forces. I can't see how a parallel will have any effect on any of this. It would be upstream and the pellets would have have "forgotten" about it.
