Preheat oven to 425 degrees F. Mince 2 green onions. Cut remaining green onions into 2-inch pieces. In bowl, toss minced green onions with pork slices, ginger, soy sauce, Worcestershire, thyme, ground red pepper, and allspice. Cover pork and marinate 30 minutes. In 6-quart casserole, toss sweet potatoes, red pepper, green-onion pieces, and 1 tablespoon vegetable oil. Bake, uncovered, 15 minutes.
Meanwhile, in skillet over medium-high heat, in 1 tablespoon hot vegetable oil, cook half of pork until browned. Remove pork to bowl; repeat with remaining pork.
Pour pineapple chunks with their juice into skillet, scraping to loosen any brown bits from bottom of skillet. Pour pineapple mixture, pork slices, and any remaining marinade over vegetables in roasting pan.
Bake casserole, uncovered, 30 minutes longer or until pork and vegetables are tender, stirring occasionally.