I recently got a sun too & also have a eclectus that not only hates the screams but picks up on the noise!
My sun was noisy but now a week ago, she still screams but they're only evening & occational morning screams. They can be controlled to limited screams.
What I found out is they thrive attention from humans. If you don't give it to them, that's what usually makes the screamers. My sun has learnt where her 'place' is in the family & has accepted this really well. She occasionally calls out to see if I'm still around & I call back.
If she has a naughty scream it's ignored & put in her cage if it gets bad until she quietens down. This has worked well for me so far. I have her cage at the end of the house in a room where I can shut the door so it doesn't drive anyone nuts & she cannot see whats going on in the house while she being put away for time out.
You can't stop the screaming but you can make it minmal. You can also try distracting the sun with other nicer noises. This didn't work with mine but I had heard that it does work. Encourage them when they make quieter noises & give them lots of praise. This is one thing that my sun is slowly but surely getting the drift of. Today when she called out to me it was a nice quiet grunt instead of a scream.
There is no doubt your AG will pick up the scream & imitate it. My ekkie has been doing this. Thankfully though, so far, it is minimal & I also know that when he finds another new noise or sound, he'll forget the scream. He lets out a complaint scream too when my sun too loud. I have lots of toys that make nicer noises to distract him from the noise, or I take him away from the noise or the conure is distracted or taken away, depending on the situation.
Since they'd be both babies, it may be easier to train both when it comes to the screaming. Also they'll grow up together which may help, but you will not be able to actually prevent the AG from picking up the sun's screams.