1. For the spice rub and pork: Combine dry mustard, brown sugar, salt, pepper, paprika, and cayenne, breaking up any lumps. Dry pork with paper towels and rub all over with spice mixture. (Roast can be wrapped tightly in plastic and refrigerated for 24 hours.)

2. Seal wood chips in foil packet and cut vent holes in top. Open bottom vent on grill. Light 50 coals; when covered with fine gray ash, pour in pile on one side of grill. Arrange foil packet directly on coals. Set cooking grate in place and heat, covered, with lid vent open halfway until wood chips begin to smoke heavily, about 5 minutes. (For gas grill, place foil packet directly on primary burner. Heat all burners on high, covered, until wood chips begin to smoke heavily, about 15 minutes. Leave primary burner on high and shut other burner[s] off.) Scrape and oil cooking grate. Place pork on cool side of grill and barbecue, covered, until exterior of pork has a rosy crust, about 2 hours.

3. For the mustard barbecue sauce and to finish: Adjust oven rack to lower-middle position and heat oven to 325 degrees. Whisk mustard, brown sugar, vinegar, Worcestershire, hot sauce, salt, and pepper in bowl until smooth. Transfer pork to roasting pan and brush 1/2 cup sauce over meat. Cover roasting pan tightly with foil and bake until fork inserted into pork can be removed with no resistance, 2 to 3 hours. Remove from oven and rest, still wrapped in foil, for 30 minutes. Unwrap pork and, when cool enough to handle, pull meat into thin shreds, discarding fat, if desired. Toss pork with remaining sauce. Serve.