I would think that maybe you letting him out when he’s screaming reinforces that behavior. He knows screaming gets him exactly what he’s looking for so of course he’s going to keep doing it. He’s found how to communicate with you so he won’t give that up easily. I’d approach him in the morning with treats that I only offer in between screams, so I’m rewarding silence. Then when he’s silent for a good while, only then does he get to come out. Ideally, you’d do this sometime before the screeching starts but I understand waking up crazy early like that for weeks would be very inconvenient. It will take a while because the screaming behavior has been so reinforced so at first he will think “I just have to screech louder and longer to get out”. But you’ll get there. In the meantime, Maybe talk to the neighbors and ask how affected they truly are while letting them know it’s a behavior you will be working on in the coming weeks.