Heat oven to 275° F. Make the rub: In a small bowl, combine the thyme, coriander, allspice, 2 teaspoons salt, and ½ teaspoon pepper.
Place the ribs on a large rimmed baking sheet. Rub the ribs with the spice mixture and tightly cover the baking sheet with foil.
Bake until tender and the meat easily pulls away from the bone, 2½ to 3 hours.
Meanwhile, make the sauce: In a small saucepan, combine the preserves, rum, lime juice, and ¾ teaspoon salt. Simmer over medium heat until slightly thickened, 4 to 5 minutes.
Transfer ¼ cup of the sauce into a small bowl for serving.
Heat grill to medium-high. Grill the ribs, basting with the remaining sauce and turning occasionally, until just beginning to char, 4 to 5 minutes. Serve with the reserved sauce and lime wedges.