Magoo;
You cut the stock correctly. The butt should be horizontally perpendicular with the barrel.
The only way to accurately pattern a gun is with the use of a bench rest similar to those used when shooting a rifle. It must allow a steady hold while aiming the shotgun like a rifle and slowly pulling the trigger as you would when shooting a rifle.
The gun is aimed while looking along the center of the rib or with the front bead appearing to rest on the center of the top of the action.
Thirteen yards is a good distance from the muzzle to the pattern board. The distance of the pattern's hole from a plus drawn on the pattern board can be trebled to find where the center of the pattern will impact at 40 yards.
If the gun shoots straight this way, you are doing something to pull your shots to the left when shooting offhand.