Mix salt, paprika, chili powder, and black pepper; rub over pork.
Put onion in a 6-quart slow cooker; arrange pork over it.
Whisk ketchup, molasses, vinegar, brown sugar, Worcestershire, and dry mustard until smooth.
Stir 1/3 cup sauce into broth; pour around meat. Refrigerate remaining sauce.
Cover; cook on low 8 to 8 1/2 hours until shoulder pulls apart without resistance.
Simmer reserved sauce in a saucepan 8 minutes while transferring, defatting, and shredding pork.
Return meat to cooker with 1/2 cup skimmed juices and enough warm sauce to coat. Serve remaining sauce alongside.