A shotgun does have to be designed to be fired from the shoulder, so there are some shotguns that (at least federally) are not shotguns but "firearms". These include the pistol grip Mossberg 500. Black Aces has a Mossberg 500 with something like an 8" barrel that is non NFA because of this. I'm not aware off hand of any single or double barrel guns that are designed this way from the factory, although it does make me think of the Ithaca Auto/Burglar which was a very interesting design.
One thing I would check is to make sure the AOW is OK with your state's laws. Although it might escape the federal definition of a short-barreled shotgun, would it meet that definition under your state law?
EDIT: The Judge (and other firearms firing shotshells) are not considered AOW because they are rifled. A rifled pistol firing a shotshell is not an AOW, only a smoothbore pistol.
If I remember correctly, Taurus tried to get approval for a version of the judge in 28 gauge but were told that it did not meet the definition of a sporting purpose, and being over .50 caliber would make it a destructive device.