KLD95 and Jed! It sounds like you have made some huge progress already!! Thanks for the tag, Michael.
Ask yourself what purpose does the screaming serve for Jed? There may be different reasons throughout the day. Commonly there is the screaming first thing in the morning and/or in the evening. This is the normal dawn or dusk chorus which means it’s good to be alive! At other times the reason could be fear, boredom or joining in with loud household noise (a running tap or vacuum cleaner). Maybe it is separation anxiety or an overzealous contact call. Or perhaps it is being reinforced either by another animal or human. Choose one instance of screaming. Can you pin point what sets the stage for the behaviour (the antecedent), and also what reinforces it /keeps it happening (the consequence)?
If the bird enjoys attention and you go to the bird to quieten the screaming/squawking (consequence), guess what you are reinforcing? Yes, more screaming. You are teaching the bird to scream every time he wants attention. If you then try to ignore the screaming it becomes worse. The bird thinks, "this worked before, I’ll just have to scream louder and longer and eventually they will come running". And what does the human do? The noise is unbearable so eventually the human goes running to the cage. You have just reinforced the louder and longer screaming!
Think of another behaviour Jed can already do that you can reinforce instead. A whistle? Talking (eg. Hello)? Ringing a bell? A whistle or talking is going to be doubly effective as a bird can’t whistle/talk at the same time as screaming. It is important Jed already knows how to do the replacement behaviour so that you can easily put it on cue when required. But do teach him other behaviours anyway... like the whispering already suggested.
Cue the whistle or other more acceptable sound BEFORE the unwanted behaviour is expected to start. And reinforce like mad!!! A HUGE amount of attention (since I am guessing this is the reinforcement for the unwanted behaviour) and maybe even treats too. EVERY TIME the bird makes the more acceptable sound REINFORCE!! You may have to drop what you are doing to come running! Later on you can drop back on the reinforcement and start answering from afar, but when teaching a new behaviour it is vitally important that you put it on a continuous schedule of reinforcement, ie. reinforce EVERY TIME!
At the same time, we need to put the old behaviour on extinction. ie. remove the reinforcement for it. No running up to the bird to quieten him. Wait until a gap in the screaming and cue the whistle. If the bird is screaming with you outside the room, wait for a gap in the screaming before you enter the room again. Then cue the whistle as you walk in and reinforce like mad!
We might look more closely at separation anxiety or an overzealous contact call if the excessive screaming starts when you go to leave the room (the antecedent). Separation anxiety is common among social creatures like parrots, especially in those that are hand reared and imprinted on humans. You can still teach the bird to whistle instead of scream using differential reinforcement as previously explained, but it is important to answer the bird’s whistle with your own whistle as you leave the room and from outside the room to let him know, "it’s ok, I am here!"
Teach him to play/forage – he needs to learn how to keep himself occupied. You can do this by providing foraging toys. Nothing complicated to begin with:
Try wrapping his favourite treats in pieces of coffee filter paper (let him watch you do it and leave some of the treat sticking out so that he catches on) and putting them into his dry/seed bowl.
Or fill his dry bowl with beads (big enough so that he doesn’t swallow them) as well as seed/pellets to get him to forage for the food.
Work up to hiding wrapped treats in toys around the cage.
String pieces of fruit and vegetables on a birdie kebab skewer (available from most pet shops) and hang in the cage.
Weave big wet kale leaves through the bars of the cage or hang them from a clothes peg. You may have to start with smaller leaves so as not to frighten the bird.
Fill lengths of coloured paper straws with safflower seed (if bird likes safflowers).
Fill woven "finger traps" with sugar snap peas and tie them to a toy.
Remember you will have to teach him how to forage in tiny manageable steps so that he gets it. Each tiny step he makes towards foraging should be reinforced.
If he is flighted let him fly and exercise to burn up energy and release feel good endorphins.
If you go out, leave the radio on so there isn’t a crushing silence.
Because Jed has learned to scream, he cannot unlearn it, but if we understand the reasons behind the unwanted behaviour we can work towards lessening it and even changing the sound to something more acceptable.