In small bowl, stir together thyme, brown sugar, black pepper, cayenne pepper, cinnamon, mustard, paprika, and salt. Set aside 1/3 of the seasoning for later use. Coat tenderloin with olive oil and then rub the remaining 2/3 seasoning onto the meat. Place tenderloin in slow cooker, then pour root beer over the pork.
Cover and cook on low for 6 hours. During this time, prep the pineapple- Place the rings in a large plastic bag with the honey, lemon juice, cinnamon, and chili powder. Shake to coat, and let marinate until the pork is almost done.
At the 6-hour mark, drain and pull pork apart with a fork. Then, return to slow cooker, stir in barbecue sauce and 1/3 seasoning from beginning, and let cook for another hour. About 15 minutes before serving, preheat your indoor/outdoor grill (or skillet, if you donít have a grill), lightly coat with olive oil, and grill pineapple for about 2 to 3 minutes per side.