Pour enough water into shallow roasting pan to come inch (1.25 cm) up side. Cut ribs into 3- or 4-rib portions; rub all over with garlic. Place single layer of ribs, meaty side up, in water. Cover and steam-roast in 325°F (160°C) oven until meat is tender, 75 to 90 minutes. Transfer to large glass bowl or baking dish, discarding cooking liquid. Let ribs cool.
Combine sugar, paprika, chili powder, cumin, salt and pepper; rub all over ribs. Cover and refrigerate for 8 hours or overnight.
To make barbecue sauce: In small saucepan, melt butter over medium heat; fry onion, stirring often, until tender, about 5 minutes. Stir in ketchup, sugar, Worcestershire sauce, vinegar, mustard, celery seed and cayenne pepper; bring to a boil. Reduce heat, cover and simmer, stirring occasionally for 15 minutes (mixture should be fairly thick). Remove from heat; brush ribs with half of the sauce.
Place ribs on greased grill over medium-high heat; close lid and grill, turning at least once and brushing with remaining sauce, until browned and glossy, 10 to 15 minutes.