Pat both sides of slabs dry with paper towels. Using a sharp knife, remove thin membrane from back of each slab by slicing into it and pulling it off with a paper towel. (This will make ribs more tender and allow meat to absorb the rub better.) Combine salt, cumin, dry mustard, and cayenne in a small bowl; rub evenly over both sides of slabs, and let stand at room temperature 30 minutes. Combine sweet chili sauce, Dijon mustard, honey, vinegar, and soy sauce.
Prepare a charcoal fire on bottom grate of a large charcoal grill. When coals are covered with gray ash, push to 1 side of grill. Maintain an inside temperature of about 300°F. (If the temperature drops below 300°F, add more charcoal as needed.) Brush both sides of ribs with 1/4 cup sweet chili sauce mixture. Place ribs on top oiled grate of grill directly over hot coals, and grill, covered, 10 minutes per side. Brush both sides of ribs again with 1/4 cup sweet chili sauce mixture, and place on grate over side without the coals. Grill, covered, 40 minutes.
Brush both sides again with 1/4 cup sweet chili sauce mixture, and grill, covered, until meat is tender to the touch and pulls away from bones on the ends, about 2 hours, brushing with 1/4 cup sweet chili sauce mixture after 1 hour. Remove ribs from grill, and brush with remaining sweet chili sauce mixture.