This is the kind of stuff that got me into smoothbores way back when!!
My grandfather when he was young was a commercial waterfowl hunter, and had a punt (which was at least 4" in diameter) and his "clean-up" double, an 8 ga. Parker. Unfortunately, the punt and skiff were sold to a collector when I was young (I got to see it once, and called it a cannon on a raft - the barrel was larger than my 2 then-young hands making a circle, fingertip to fingertip), but the Parker is still in the family (perhaps because the stock was repaired 3x over its lifetime, and it's a commercial gun, not a fancy looker...)... When dad died I inherited the 8 ga, and contemplated restocking it so it could be used again (for show only :grin: )...
What you have may well be a "clean up" gun - designed to take out the wounded in a flock taken by a punt. The shortened stock is what's making me think this - easier to have on a hunters skiff and bring to bear after firing the punt. The objective back then for people like granddad was to bring in as many birds as they could to put on the meat counter that day. The punt was heavily loaded to take out as many birds as possible, the clean-up to take out the birds left by holes in the pattern.
As a side note - my dad remembered as a young boy having to pluck and clean piles of birds for market that day, and while he (and the rest of my family) were and are avid (maybe rabid!) waterfowlers he HATED plucking and cleaning. He'd do it, and he was darned good and damned fast at it... but you knew that was NOT the time to ask him a favor!
Still, what you have is a pretty nice piece of history... It'd be fun to see what it looks like once the rust has been arrested and you can see what's going on there, even more fun to see how she patterns. Thanks for showing us!