Check the ballistics charts. The 20 is more than capable of taking deer or moose for that matter out too 150 yards, much less recoil is a bonus. When slug gun technology first broke on the seen I was sold on 12 ga 3" sabots.
After realizing 3 in slugs hurt when practicing and no fun I dropped back too 2 3/4s. A 20 guage is perhaps perfect for what you describe.
JW