Paul Revere: lots of good points in your post "put a sling on that shotgun and use it for all of your shots, wrapping it around your brace hand forearm. When not shooting offhand in the field, put your barrel against a solid surface when sighting (like a tree) and exhale slowly as you squeeze the trigger."
I just have to disagree on one minor point. You shouldn't put the barrel itself against a solid object. Better to rest the gun on a hand that rests on the tree or other solid object. Otherwise, vibration in the barrel can change your point of impact.