I've been in the same boat for years. I like the idea of a 20ga shotgun pistol without the BATF paperwork, or price of the Hawdaw.
One potential option that came to mind, is to find a decent big bore pistol, such as a .54 or .58 cal (preferably one with a rusty bore so ya can buy it cheaper!), and then have a machine shop ream the rifling out of the barrel. A 5/8" drill bit/reamer is .625", which should be close enough for this purpose to still use 20 gauge wads. Ballistic Products sells wads that are slightly oversized, too.