I tried using smaller gauge shotguns and went back to the 12ga and adjust my loads to what I want. I have sxs 12s as light as 5 lb 15 oz and I have loads as light as 11/16 oz for my 12s and more st a f my sxs have plastic or steel butt plates. I still have a couple 16s but they weight the same as my 12s and shoot the same weight loads.
I have a pile of light 12s that I've gathered over the past few months to use as prize guns at our RGS Chapter events. If I were struggling with recoil issues, that's the direction I'd go.
My 16 (Poli) is 6 lbs, and it's no fun for 100 clays. I'd much rather shoot my 8 lb AyA Model 53. Horses for courses, IMO.
My daughter has been shooting with me off and on for a few years, and started out with a 6 lb. 20 gauge Superposed lightning...she's finally getting good enough that she's noticing the light gun with short barrels is costing her targets. I recently got her a 12 gauge Superposed Lightning with 28" barrels that tips the scales at 7.7 lbs...she can tell just by picking it up that it'll help. The added weight will help recoil too.