Jerry, as I read this the gun is held static and the laser is concentric with the bore at the muzzles. If that's correct then I question how your methodology translates to actually shooting said shotgun from the shoulder.
Your tests don't account for “barrel time” = milliseconds during which the muzzles rise while the shot travels down the bore. That begins at the instant of firing when the gun starts to recoil. Barrel time will vary with different velocities and thus the muzzle rises less or more before the shot emerges, depending on the shells being fired. And all that in turn affects the POI versus the "point of aim" just before firing.
Also, how about the torque/twisting effect when the gun is fired? Left barrel will have less sideways movement than right barrel (for a right shoulder shooter). Vice versa for left shoulder shooters. Again that will affect the POI.
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