Rinse and pat ribs dry. If desired, remove thin membrane from back of ribs by slicing into it with a knife and then pulling it off. (This will make ribs more tender.)
Rub ribs with cut sides of limes, squeezing as you rub. Massage ginger mixture into meat, covering all sides. Wrap ribs tightly with plastic wrap, and place in zip-top plastic freezer bags or a 13- x 9-inch baking dish; seal or cover, and chill 8 hours. Let ribs stand at room temperature 30 minutes before grilling. Remove plastic wrap.
Light 1 side of grill, heating to medium-high heat (350° to 400°); leave other side unlit. Place rib slabs over unlit side, stacking 1 on top of the other.
Grill, covered with grill lid, 40 minutes. Reposition rib slabs, moving bottom slab to the top, and grill 40 minutes. Reposition 1 more time, moving bottom slab to the top; grill 40 minutes.
Lower grill temperature to medium heat (300° to 350°); unstack rib slabs, and place side by side over unlit side of grill. Cook ribs 30 more minutes, basting with half of Sweet-Hot 'Cue Sauce. Remove ribs from grill, and let stand 10 minutes. Cut ribs, slicing between bones. Serve ribs with remaining Sweet-Hot 'Cue Sauce.