Sorry for the slow response, but just to support the previous wise sages before me...
Your shotgun may have a major headspace problem, and that it is most noticeable because of the test fired shells which had no propellant or shot (post#12). A good question is why the tester didn't fail this gun.
From the Speer Reloading Manual 13, Primer Appearance, pg. 54
"Primers that back out of the pocket seldom indicate a high pressure condition. In fact, the opposite is true; low pressure is likely the culprit. All sporting firearms have a certain amount of clearance between the breech face and the cartridge. This allows for a little room for powder residue and dirt to accumulate that may prevent a malfunction when the firearm is used under dirty conditions. When a primer fires, it generated its own level of pressure even before the propellant charge fully ignites. This initial pressure causes the primer to back out of the primer pocket until it is stopped by the breech face. When the propellant charge reaches normal pressure, the cartridge case is driven back until it is also stopped by the breech face and the protruding primer is reseated. If the operating pressure is low, there isn't enough force to drive the case back and the primer remains backed out."
And
"Excessive headspace can cause severely flattened primers at safe working pressures because the primer backs out much more than normal before the powder charge ignites."