Although stimulants like Concerta can be effective once they have kicked in, they won’t improve your boys’ early-morning raucousness. Perhaps substituting or adding a non-stimulant would provide more around-the-clock coverage.
The simpler option may be to do what you already suggested — put locks on the outside of the doors. Explain to them that you worry about their safety when they roam around the house unsupervised. You may need to give each of them a potty to use in their room in order to prevent trips to the bathroom. Tell them that if they wake up early, they can play quietly in their room.
Once they show that they won’t leave their room — it might only take a couple days — remove the locks. By showing them that you are serious about curbing their early-morning escapades, they may be more receptive to the rewards and consequences you have already tried.
“Dropping the Discipline Hammer On My Teen Son”