Make shallow cuts between the ribs on the bone side with a sharp knife, piercing just the membrane.
Mix 1 tablespoon salt, the brown sugar, garlic, thyme, chili powder, 1/4 teaspoon black pepper and the cayenne in a bowl. Rub the spice mixture evenly over the ribs. Place the ribs on a rack in a roasting pan, loosely cover and refrigerate at least 4 hours or overnight.
Meanwhile, combine the cider, ketchup, mustard and Worcestershire sauce in a saucepan over medium heat and simmer until reduced to about 2 cups, about 30 minutes. Cover and set aside.
Preheat a grill to low heat on one side. Cook the ribs bone-side down on the cooler side of the grill, covered, until tender, about 2 hours 30 minutes. (If using a charcoal grill, add more charcoal as needed to maintain the temperature.) Continue to cook, uncovering every 10 minutes to baste with the sauce, until the ribs are glazed, about 40 more minutes. Remove from the grill and cut into pieces.