Boy do I hear you, and I feel for you. A year and 1/2 ago, I adopted from an elderly couple our Sun Conure. The first few months he was great! Then he started screaming a bit, then a bit more and then it was almost NON STOP through out the day.
It was enough to make you want to rip your hair out! I/we tried EVERYTHING, moving him throughout the house, covering and uncovering his cage, letting him be out all day, trying to redirect his screaming with talking, toys, treats, you name it, I tried it, I even came here a posted a few months ago and didn't get a chance to follow it up...but Sunny was truly on his last feather around here.
Finally one day in my frustration I moved him into our office and I shut the door to muffle the sound...I just couldn't take it any more! Turns out...Sunny LOVES the office! He is such a happy camper now and the difference in his personality is like night and day!
He is 4 1/2 years old and I don't know if his screaming was just a "teenage phase" and all sun's go through it, or if he was just over stimulated.
I believe it might be a little of both, but more leaning toward the over stimulation. We have a very very busy household and instead of enjoying being in the center of the action, he was incredibly overwhelmed and his stress came out as screaming.
He has been living in our 'office' now for a couple months. We are in and out all different times through out the day to use the computer, so it's not like he's been cast to some lonely room with no attention.
He pretty much never screams anymore...and if he does seem to start feeling overwhelmed and starts squawking out of the "norm" we will simply shut the door and let him have his space.
Finally...we found balance and we are all happy!
It's not the arrangement I wanted for him, I really thought he'd love being out with the other birds and in the hub of the house where all the action takes place...but what I thought and what he apparently wanted were two different things.
I am so happy to have found this solution and it's working great for now. I truly love the little chap and hope I can do what it takes to continue to keep him happy.
I know it doesn't seem like much help, it's hard to know what could be causing your guys' screaming. But try moving his cage to other area's of the house, maybe, quite by accident you will find a place he seems to prefer to be and he will quiet down to "normal" conure chatter/calling.
Toni