Huntingbull,
I have a 20 guage H&R break action single. It is Modified choke. On it I mounted a 2x Bushnell scope in Weaver rings. It is light and shoots aboout like your old 12 guage.
The 20 guage is SUPER light and with the 2 3/4 inch super X slugs is good deer killed. It shoots thru on deer out to about 80 yards. I made it up because of some urban areas that I hunt that are shotgun only, seldom do I get a shot over 50-60 yards so it works fine. On whitetail around here you only get a single shot, then they are just tails.
I'd think any used gun shop or pawn shop would have an old H&R single, they are usually full choke. But a few seconds with a hacksaw and you could cut off the last 3 inches and you would have a full choke. WATCH STATE GUN LAWS ON SHOTGUN LENGTH BEFORE YOU CUT. The muzzle can be crowned with some medium sand paper by spinning it in your hands. The barrel is soft and very easy to tap for a scope or sights.
Add a set of sling swivels and you are home. If you put the scope on I'd add a hammer spur/extension.
If you like the smooth bore you can look for a Savage single that is hammerless and has a thumb/tang safety. These were marked under the Model 320/319 and other model numbers...no hammer merely slide the safety off and ...instant venison.
BEAR