In a large bowl, stir together the salt, garlic powder and black pepper. Add the meat and rub the mixture all over the pork. Cover with plastic wrap and refrigerate for at least 3 hours or overnight.
In a small saucepan, combine the vinegar, ketchup, brown sugar, Worcestershire sauce, mustard, chili powder and cayenne. Simmer over low heat for 5 minutes.
Place the pork in a slow cooker. Pour over two-thirds of the vinegar mixture. Cook until the meat is falling-apart tender, 7 to 8 hours on low heat or 4 to 5 hours on high.
Remove the pork from the cooker and place on a rack with a rimmed baking sheet placed underneath. Let stand until cool enough to handle.