Heavy Barrel has no effect on shotguns
As a test it would be interesting to see Heavy Barrel get the added benefit of reducing shotgun spread, now that Improved Rifling murders TTK -10 / 20 / 30% Accuracy loss -5 / 10 / 15% Shotgun pellet spread ( a far cry from the DOW's 35% ) -5 / 10 / 15% weapon damage It'd prioritize aiming properly since you need to make up the damage loss by hitting more pellets, and their CQC effectiveness will also be reduced, as tighter spread = need better aim = less likely to hit partial shots unless your aim is on point
The effectiveness at range would still be kept in line by the damage reduction, seeing as shotguns don't have great drop-off ranges