Well explosive rounds are another problem - iirc there is a $200 destructive device 'tax' for everything that goes 'boom' outside a barrel.
Not sure if there is anything that outright bans modern artillery, but they would be over the .50 caliber limit and not a shotgun - therefore subject to more regulations.
Been a long time since I;ve read about cannon ownership but I believe old style cannons are allowed due to them being black powder devices.
Yes, I've ready stories about these "cannon shoots". Sounds like fun.
Anything over .5" and not a "sporting" shotgun. Twelve-gauge shotguns that are deemed "unsporting" by the BATF are taxed as destructive devices.
I'm somewhat surprised that nobody's come up with a good bull-pup 28ga shotgun for home defense. A fixed choke could have a diameter of 0.495" so as to avoid the "destructive device" classification, and a 28ga shell should provide a somewhat useful payload (especially if there were standard 3.5" and 4" lengths).