Prepare a large two-gallon storage bag (or other container that will fit the ribs). If your racks of ribs are too large, you can cut them in half along one of the bones, but try not to disassemble them too much. Ribs cook best when left as whole as possible. Rub the ribs down with the salt, sugar, and jerk seasoning.
Combine all of the ingredients of the marinade in a small measuring cup. Place the ribs inside the storage bag, cover with marinade, and refrigerate for at least 2 hours or up to overnight.
Preheat the oven to 325°F. Line a baking sheet with foil, and set an oven-safe cooling or grill rack inside of it to elevate the ribs while cooking. Arrange the ribs on the baking sheet, and cover them with foil.
Cook the ribs for 2 hours covered in foil, flipping on the hour. During this time, make the Molasses Glaze. Combine all ingredients except for the rum in a medium saucepan over medium heat and bring to a boil. Reduce the heat to a low simmer, and cook for 30-45 minutes, until thickened. Stir the rum into the glaze, cook one minute more, and remove from heat and keep warm.
Once two hours have passed, uncover the ribs, flip again, and coat the ribs with some of the glaze (You should reserve plenty of glaze for drizzling on the ribs before serving). Put them back in the oven, uncovered, for an hour. Flip and re-glaze the ribs at the half-hour mark. When the time is up, check the ribs for doneness – the meat should pull easily away from the bone. If it does not, re-glaze and cook for an additional 15 minutes, repeating until done.
Remove the finished ribs from the oven and place on a cutting board to rest for 5-10 minutes. Slice the ribs. Serve on a large platter and put out a bowl with the remaining Molasses Glaze on the side for dipping.
