We shoot a lot of 20s, mainly Remington 870s. We're able to get killing patterns out to 40 yards with the SSX and 3" Hevi-13 shotshells with 1.25 oz. of #6 shot. That is with 26" and 28" barrels however.
It's much more of a challenge with the shorter barrels. Doris has a 20 gauge 11-87 with a 20.5" barrel that I "deep cleaned" and with the SSX and those shells, it will deliver a good even pattern at 40 yards. We did have to put some open sights on it because it did not shoot to point of aim however.
I'd say after deep cleaning your barrel and choke(Truglo SSX?), the best thing you can do to improve those patterns would be the shells.
"If he's out of range, it just means that he has another day and so do you."