Shotgun shot is not armour piercing, the lower level protection vests would suffice. From far enough away a heavy parka would stop shotgun pellets.Most of those cases mentioned above it seems to me the unaffected armors would be sufficient, some of them even preferable.
Honestly, the best argument for level III armor I can think of is one nobody seems willing to make: Hunting accidents frequently involve shotguns, sometimes at very close range, and while I can't find much information on what kinds of body armors are effective with shotguns, I would imagine concealability isn't a concern but maximum protection is. I know it's a long way from the narrative gun rights groups want, but that kind of drunken stupidity does happen. A lot. Consider a particular vice president who showed an epic disregard for the 10 o'clock rule and muzzle sweep discipline, and imagine if the same mistake had been made hunting deer instead of birds.