What most people don’t realize is the 20 has as much “killing” energy as a 12 when the proper shells are used. 6 shot going 1250fps is the same whether it’s coming out of a 12 gauge or a 410. The only difference is the payload or the amount of shot. Just a smaller margin for error with the smaller gauges.
I too have a right bad right shoulder and so have switched from my tried and true 12 gauge o/u to my grandfathers Remington model 11 20 gauge auto for all my small game hunting. I still use my 12 gauge Valmet 412 O/U for turkeys because it is usually a one shot deal, but I am looking to get a 20 gauge barrel for it. My daughter hunts turkeys with a 870 Remington 20 gauge and it gets the job done. My grand niece has taken 3 mature gobblers this year with a 20 gauge auto this season and she is seven years old. She also took a 10 and 9 point with a 223 this past deer season.