I'm not equivocating, I'm educating.
Again, you are incorrect, there is very little difference in the pattern. The pattern is almost entirely a function of the choke. Now it's true that if you cut off the barrel of a full or modified choke 20" barrel (not that a 20" barrel is likely to have anything but a cylinder choke, that is no choke at all) and don't install a choke tube, you will get a wider pattern, since you will have changed chokes. But most 20" shotguns, and my 18.5" one, already have cylinder chokes.
IIRC, correctly about the shortest choked barrel I've seen was a 21" Remington 870 Upland Game model, but even for upland game, or skeet, most folks like a 24 or 26 inch barrel. When I hunted with the fellow who owned it, another hunter in the group asked him if he was going to shoot pheasants with it, or rob a bank with it. :)
Mine is 24", and my father in law, who had an otherwise identical Browning, was jealous, and wanted to trade barrels, even though his is only 2" longer. :) Both of them have screw in choke tubes, so they can have most any choke we want. I have tubes for Full, Modified and Improved Cylinder. IC is still some restriction.
The real advantage to a short shotgun is that is more handy. You can more easily use it in confined spaces, such as inside or coming out of a vehicle, or in your hallway.
I salute you for your persistence, but, really, in this case it's like trying to bail out the Pacific Ocean with a teaspoon.