I really sounds like your way over thinking this. A nice vierling would do the trick. 16ga/16ga/7x65R/22LR or Hornet. Flip up open sight for the 22LR and a nice1-4x20mm scope in claw mounts for the 7x65R. I guess someone is ahead of you by nearly a hundred years. You can also get an adjustable rimfire insert for one of the shotgun barrels on a regular drilling.
Then there is always a Bockdrilling if a single shotgun barrel is sufficient..
When folks talk about combo guns they think big 12ga which is far off track, really a 2 3/4" 16ga will accomplish everything you need in a shotgun. If the game is too far away to kill with a 2 3/4" 16ga you have the rifle just a trigger or selector away.
I regularly hunt coyotes with a 2 1/2" 16ga loaded with 1 oz. NP BB's, kills them dead under 40 yards over that I switch to the rifle barrel.
What you've described sounds like a 12 pound behemoth that would handle like a chunk of scrap iron. With 16ga barrels you can have the most versatile drilling that with the scope off handles like a fine bird gun.
This is just a 2 3/4" 12ga/5.6x50R combo gun, 1 1/4 oz. NP BB's work perfect for coyotes.