In a large bowl, combine the sugar, coffee and 1/2 cup of salt. Add the pork and rub the mixture all over. Cover with plastic wrap and refrigerate for 12 to 24 hours.
Preheat the oven to 300°. Rinse off the pork and set in a roasting pan. Roast the pork for 6 hours, basting with pan juices, until an instant-read thermometer inserted in the thickest part registers 200°; cover with foil for the last 2 hours of cooking. Transfer the pan to a rack and let rest for 30 minutes. Increase the oven temperature to 500°.
In a saucepan, boil the sorghum and vinegar; season with salt and pepper. Simmer until slightly reduced, 10 minutes. Pour the glaze over the pork and roast for 15 minutes, until glazed. Let cool, then shred the pork.