Combine all ingredients except steaks. Arrange steaks in single layer in roasting pan; pour soy sauce mixture over steaks. Marinate 3 hours, turning steaks after 1 1/2 hours. Drain off marinade; bring to a boil; reserve for sauce.
For each serving, to order: Spray heated griddle lightly with nonstick cooking spray. Grill steaks on each side to desired degree of doneness, turning frequently. Serve each steak with 1/4 cup sauce.