1. Combine kosher salt and next 2 ingredients. Remove thin membrane from back of ribs by slicing into it with a knife and pulling it off.
2. Rub ribs with cut sides of limes, squeezing as you rub. Massage salt mixture into meat, covering all sides. Wrap tightly with plastic wrap. Place in a 13- x 9-inch baking dish; cover and chill 8 hours.
3. Light 1 side of grill, heating to 350° to 400° (medium-high) heat; leave other side unlit. Let slabs stand at room temperature 30 minutes. Remove plastic wrap. Place slabs over unlit side of grill, stacking one on top of the other. Grill, covered with grill lid, 40 minutes. Rotate slabs, moving bottom slab to top; grill 40 minutes. Rotate again; grill 40 minutes.
4. Lower grill temperature to 300° to 350° (medium) heat; place slabs side by side over unlit side of grill. Baste with barbecue sauce. Grill 30 minutes, covered with grill lid, basting with sauce occasionally. Remove from grill; let stand 10 minutes.