Make marinade sauce by combining chopped onion, chopped garlic, chopped parsley, Worcestershire sauce, steak sauce, dry mustard, and Tiger sauce. Mix well.
With a sharp knife, make cross slits into top of pork roast and rub sauce into the roast. Refrigerate overnight.
Mix tomato paste and the brown sugar very well and set aside.
Set one grid at the highest setting and the others at the lowest setting. Set the burner to medium heat under the high grid. Wrap roast in heavy-duty aluminum foil. Place an oven-safe meat thermometer into the heart of the roast. Cook with lid closed or partially closed until the internal temperature is 170ºF. As the roast approaches the internal temperature, open the foil and coat the top of the roast with a mixture of the tomato paste and brown sugar. Place apple wood chips on top of the flavor screen during last 30 minutes of cooking. Remove roast, brush with tomato paste mixture, carve, and serve.