Combine the salt, paprika, chili powder and black pepper and rub the mixture over the pork.
Put the onion in a 6-quart slow cooker and arrange the pork over it.
Whisk the ketchup, molasses, vinegar, brown sugar, Worcestershire and dry mustard until smooth.
Stir 1/3 cup of the sauce into the broth, pour it around the meat and refrigerate the remaining sauce.
Cover and cook on low until the shoulder pulls apart without resistance, 8 to 8 1/2 hours.
Simmer the reserved sauce in a saucepan for 8 minutes while you transfer, defat and shred the pork.
Return the meat to the cooker with 1/2 cup skimmed juices and enough warm sauce to coat it, then serve the rest alongside.