Combine the onion salt, paprika, 1 tablespoon of the brown sugar, the chili powder, allspice and black pepper in a medium mixing bowl. Reserve 1 tablespoon of the spice mix; rub the remaining spice mix all over the pork. Wrap the pork in plastic wrap and refrigerate for 1 hour or overnight.
Heat the oil in a large skillet over medium-high heat. Add the pork and cook, turning to brown it on all sides; this will take about 16 minutes. Transfer to a 4- to 5-quart slow cooker.
Add the vinegar, the reserved tablespoon of the spice mix and the remaining 3 tablespoons of brown sugar to the skillet; as the mixture begins to boil, use a wooden spoon or spatula to dislodge any browned bits on the bottom of the skillet. Transfer the mixture to the slow cooker.
Cover and cook on LOW for 6 to 10 hours, until the pork is fork-tender.
To serve, remove the pork from the cooker and cut it into 1/2-inch-thick slices, then use 2 forks to shred the slices into bite-size pieces.
Add the hot pepper sauce to the liquid in the cooker, then return the pork and any accumulated juices to the cooker and toss to coat with the liquid. Serve warm, or keep warm for up to several hours.