Preheat oven to 350°F with racks in upper and lower thirds. Place each rib slab on a separate large sheet of heavy-duty aluminum foil (if you don't have heavy-duty foil, double up regular foil). Season ribs on both sides with 2½ tablespoons salt and 2 teaspoons pepper. Fold each sheet of foil around each slab, crimping foil at the sides and top to seal completely. Place 2 rib packets each on 2 baking sheets. Bake until ribs are fork-tender, about 2 hours.
Remove ribs from oven and very carefully unseal each packet (the steam inside will be very hot). Let ribs cool in foil to room temperature, about 1 hour. Pour out any juices in packets, reseal foil, and refrigerate for at least 4 hours and up to 24 hours.
Whisk tomato puree, pomegranate molasses, honey, vinegar, tomato paste, mustard, paprika, cayenne, and remaining 2 teaspoons salt and ½ teaspoon pepper in a medium pot. Bring to a simmer over medium-high. Reduce heat to medium low; partially cover and simmer, stirring occasionally, until slightly thickened and reduced to about 2½ cups, about 15 minutes. Let sauce cool to room temperature, about 1 hour. Use immediately or refrigerate, covered, for up to 24 hours.
Preheat grill to medium-high (400°F to 450°F). Working in batches if needed, remove ribs from foil packets and place on oiled grill grates. Grill, flipping ribs and basting generously with sauce every 3 to 4 minutes, until ribs are hot, well-sauced, and browned and crisped in spots, 12 to 15 minutes total. Remove ribs from grill; let rest for 5 minutes. Slice and serve.