Bump on your search. Consider reloading if you dont already. You can load 12ga with 3/4oz loads that will smoke skeet targets but shoot softer than a 28ga (out of a 12ga frame). You also save money on ammo as shot is the most expensive component by far.
In an o/u you dont have to worry about ejection, so reloading is very forgiving. Also add weight to your gun. Recoil = equal and opposite reaction. My skeet gun was around 8.5 lbs
The only thing that may shoot softer is a semi auto 28ga, but ammo is very expensive unless you reload.
Often times the smaller guns also scale down the frame, so a lightweight 20 is going to shoot just as stout as a heavier 12ga. Just something to consider! Good luck on your search