1. Soak hickory chunks in water to cover at least 1 hour; drain. Place 3 cups wood chunks in center of each of 2 large squares of heavy-duty aluminum foil; fold each into a rectangle, and seal. Punch holes in tops of packets.
2. Light one side of grill, heating to 250° to 300° (low) heat; leave other side unlit. Place 1 packet on cooking grate over lit side.
3. Meanwhile, remove thin membrane from back of ribs by slicing into it with a knife and then pulling it off. Combine dry rub and brown sugar; rub mixture over both sides of rib racks. Place ribs, bone side down, over unlit side, and smoke, covered with grill lid, 2 hours. Add remaining packet of hickory chunks to lit side of grill. Turn ribs over; cover and smoke 2 more hours.
4. Preheat oven to 300°. Cut ribs, slicing between every 3 bones; place in a large roasting pan. Pour barbecue sauce over ribs. Sprinkle with watermelon cubes; tightly cover pan with aluminum foil. Bake at 300° for 2 hours or until ribs are tender. (Meat should separate easily from bone.)
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