As noted above you've going to need to do a bit of testing (patterning) with whatever shorty you employ - and that goes for the weapon, the round, and the shot size... Some years ago the trainers for Dade county's officers (Miami, etc.) did a bit of testing with improved cylinder bored, standard riot guns using basic 2 3/4" 00 buck rounds and found them to reliably disperse the shot at one inch per yard from the muzzle.... a seven inch pattern at seven yards (one foot past that 20 foot requirement). As a practical matter, it meant that if you weren't aiming - you weren't hitting...
Their means used to demonstrate how it went were sequential targets (just 2 x 3 foot blank white targets placed at 3, 7, and 15 yard intervals, one behind the other in a straight line to show exactly what was happening as that load went downrange. Very enlightening.
Although you may believe you want that pattern to expand as you've indicated... me, I'd want as many of those pellets on target as possible for an immediate end to any conflict... I'd vote for that 7 inch pattern every time - but I'm not an advocate of short barreled shotguns at all... I'd want and prefer a standard riot gun every time, if I had a choice, for close quarters work (since in the real world getting your target to remain stationary isn't something I'd ever expect). No matter what is shown in popular entertainments.....