In a 5-to-6 quart slow-cooker bowl, combine paprika, mustard powder, 1/4 cup brown sugar, 1 teaspoon salt and 1 tablespoon freshly ground black pepper. Add the pork and rub mixture all over meat. Arrange pork in single layer in slow-cooker bowl, fat side up.
In medium bowl, whish vinegar, ketchup, red pepper, 1 teaspoon salt, 1 teaspoon freshly ground black pepper, and remaining 1 tablespoon brown sugar. Pour 1/2 cup sauce into large bowl; cover and refrigerate. Pour 1 cup water and remaining sauce into slow-cooker bowl. Cover slow-cooker with lid, and cook on low for 8 to 10 hours or until meat is fork-tender.
Carefully transfer meat to large bowl; remove fat and skin and discard. Using two forks, shred meat into small pieces. Carefully pour sauce from slow cooker into fat separator. Pour half of sauce over meat and pour remaining sauce into gravy boat. Discard fat.
When ready to serve, remove reserved sauce from refrigerator; with fork, whisk in mayonnaise. Add coleslaw mix, and toss until well combined. Divide meat among bottoms of buns, top with coleslaw, then add bun tops. Serve with reserved sauce on the side.