OK so you're stuck between a rock and a hard place it would seem depending on the definition of what really is a shotgun with a rifled barrel.Short range weapon is archery, muzzle loader, shotgun and handgun using cartridges originally developed for a handgun.
When you consider the accuracy that can be achieved with rifled slugs that could be the simplest solution providing your ranges aren't excessive.
When I think about all the deer I've taken under 50yds...................closest was just 4 and taken with a hip shot from a 308 !