Don’t really want to start a debate here, but have you ever shot a Mossburg 12 ga. Sluggster with a slug or double ought buck? You will not want to pull the trigger again! After careful consideration, I believe a 20 gauge double barrel coach gun will do the job in the house with Short range fields of fire. And you will not hesitate to reload and shoot as many times as necessary.. just my two cents.
I agree with your observation of the efficacy of 20 Gauge for the scenario that you described. I would like a bit more punch at range with high velocity #8 shot out to 50 yds, and High velocity 1600 fps slugs at 100 yds. As you know, velocity, effectiveness, and accuracy with shot and slugs degrades rapidly beyond 25 yards. This is mitigated a great deal by high velocity 12 gauge shot.
My experience with shotguns is quite extensive with Remington 870 and Mossberg 590 pump guns as a police officer, and Benelli M4’s in the armed forces. I am used to handling their recoil.
I agree that one should extensively practice with a 12 gauge before relying upon it for serious social work. PRACTICE PRACTICE PRACTICE is all!!!!