Check the AVE schedule to Chamartín as well. It's only like 3 hours from Asturias to Madrid on the train and then 15 minute ride to the airport (you can do by cercanías if you have extra time or get an uber/cabify to get right to the door)

Could easily be the better option since you have luggage with you the whole time and you can leave right from Oviedo or Gijón city center.