1. Mix sugar and seasonings; rub onto meat. Cover with plastic wrap; refrigerate at least 1 hour or up to 24 hours. Meanwhile, soak wood chips in water 1 hour; drain.
2. Arrange charcoal on bottom grill grate evenly on both sides of foil drip pan. Light charcoal. When coals are hot, sprinkle with 2 cups wood chips. Place meat on top of grill grate, fat-side up, in center over drip pan; cover. Grill 3 hrs, turning after 1.5 hours and replenishing wood chips.
3. Remove meat from grill; wrap in double layer of heavy-duty foil. Return to grill; grill 1 hour or until meat reaches 200 F. Remove meat from grill; carefully unwrap foil at top.
4. Mix remaining ingredients; pour 3/4 cup over meat. Wrap loosely with foil. Let stand 30 mins. Transfer meat to cutting board; cut across the grain into thin slices. Serve with remaining BBQ sauce mixture.