Pressure blows out the barrels almost instantaneously. Your gun would be beat to pieces more slowly.
The pressure to pop the barrels is high instantaneous psi, whereas recoil is in momentum units.
Maybe rocketman can clearly explain radial pressure versus time and overlay it on a recoil vs time graph. One happens before the other, in a perpendicular direction to the shotgun holder.

Out there doing it best I can.