Slide a butter knife under the membrane on the back of the ribs, grip it with a paper towel and pull it off.
Cut each rack into three- or four-bone sections and rub the pieces with the smoked paprika.
Whisk 1 1/2 cups barbecue sauce with the vinegar and brush half of it over the ribs.
Stand the rib sections around the wall of a 6-quart slow cooker, cover and cook on low until tender but not falling apart, 6 1/2 to 7 hours.
Transfer the ribs carefully to a foil-lined sheet pan and brush them with the remaining sauce.
Broil until the sauce bubbles and darkens at the edges, 3 to 5 minutes.
