Mix paprika, brown sugar, salt, garlic powder, onion powder, black pepper, mustard, and cayenne.
Reserve 1 tablespoon rub; coat pork thoroughly with rest.
Spread onion in a 6-quart slow cooker. Add pork; pour apple juice and vinegar around meat.
Cover; cook on low about 8 hours until very tender.
Transfer pork to a rimmed pan; discard excess fat. Pull into thick shreds.
Toss pork with reserved rub and 1/2 cup skimmed cooker juices.
Spread half the pork on a foil-lined sheet. Broil 3 to 4 minutes until scattered edges brown; mix back with soft pork.