1. Juice lime (1 tablespoon). Combine lime juice, ginger paste, and 1 cup jerk paste. Find seam in pork roast and cut down center to lay flat. Pound lightly with meat mallet until 2 inches thick, then score pork on both sides with ½-inch-deep cuts spaced about 1 inch apart. Rub jerk mixture into pork (wash hands). Cover and chill 2 hours (or overnight) to marinate.
2. Preheat grill on medium-high. Grill pork 8–10 minutes on each side until charred. Reduce grill to medium-low for indirect grilling. Place pork fat-side up on cool side of grill. Cover and cook 1 ½–2 hours, turning and rotating occasionally, until 185°F (for sliceable). Remove pork from grill and let rest 30 minutes.
3. Combine barbecue sauce, steak sauce, and remaining ½ cup jerk paste in small saucepan. Bring to a simmer and cook 5 minutes. Slice pork and serve with jerk barbecue sauce.

Chef's Tip: After charring, you can alternatively place pork and 12 oz water in roasting pan, cover tightly with foil, and bake at 350°F for 90 minutes or until tender and 200°F (for shreddable).