Combine drained canned beans, fully cooked sausage, onion, bell pepper, celery, garlic, paprika, thyme, cayenne, salt and pepper in a labeled gallon freezer bag. Remove excess air and seal.
Freeze before slow cooking: lay the bag flat on a tray and freeze for up to 2 months. Keep broth and rice separate until cooking day.
Thaw the sealed bag in the refrigerator for 24 hours. Empty into a 6-quart slow cooker and add broth.
Cover and cook on low for about 6 hours until vegetables are tender and the mixture is hot throughout. Mash about 1 cup beans against the side, stir them back in and cook covered on high for 15 minutes.
During the final 30 minutes, bring rice and 2 1/2 cups water to a boil in a covered saucepan, reduce to low and cook for 15 minutes, then rest covered for 10 minutes.
Divide rice and thickened beans among 6 bowls, distributing the sausage evenly.
Refrigerate leftovers in shallow containers within 2 hours and reheat covered in the microwave, stirring midway, until the beans, sausage and rice reach 165°F.