Awwww...I'm so sorry to read that you are having such a difficult time with your conure. We have a yellow sided green cheek...Franklin...he adopted us when he was just 2 1/2 months old and from somewhere in the 8-9 month range, he became quite a little "bully butt" as I put it.
We got through it, but I made some changes. So here's what worked for us and we've had a very successful relationship with Franklin for over a year now...infact, the end of May 2013, he'll have owned us for 2 years.
One was, intially his cage was placed on a dresser which made his highest point, over our heads and his lowest point about our upper chest. He would do the same thing as far as begging to be out, I'd go over, open the door, offer my finger and he'd land baste with a stout bite so hard! And NO WARNING! He'd act like he was totally going to step up and WHAM!!
I read everything i could get my hands on and one article essentially mentioned that when birds are "higher" than you, they feel in control, they are the 'boss' and sometimes curbing aggressive behavior is simply lowering their living space to your face or lower, making you larger and them NOT the 'boss'.
Of course that went along with not allowing them on your shoulder or head.
If your cage is situated above your head you might try lowering it.
After we lowered Franklin's cage if he bit my finger on our initial step up, then I'd tell him in a firm voice...OUCH..NO BITE and shut the door and walk away and try again later. Sometimes it was 10 min's later, sometimes hours later, depending on how busy I was that day. The final straw was when he spent 3 days in his cage without coming out because every time I tried, he bit...then one day...I tried again, he was very timid...I was scared, but tried not to show it...he reached out like he was going to "test" me and I told him in a warning voice...beee nice...and when he didn't bite I said...GOOD BOY!! and it took a few minutes of me standing there...him thinking the process through...and finally...voila! He stepped up and I took him out and we had the best evening!
The other thing I considered when I read your post was, he sounds like he could be cage bound and have you ever just opened your cage door and let him come out on his own? Let him play and release some energy before you try to handle him? He sounds like a bundle of energy and conures are notorious for getting a bit bitey when they are over excited. This might help too.
Our Franklin is 90% perfect when he comes out of his cage now...every time...we haven't been bitten in over a year now...the other 10 percent of the time, I can usually tell if he's "on edge" I'll open his cage door and walk away...I don't wait, I don't offer up my attention at all...and he comes out and after a few minutes, when he's on top of his cage and less "agitated" looking, I can go over and offer my finger and he hops right on.
The other thing that worked with Franklin was when he was out with us, (we had him coming out of his cage good, but he'd still want to bite/attack when out if over stimulated) so if he got over excited or just flipped out psychotic and tried to attack...I'd grab a towel, t-shirt, blanket...what ever was handy and toss it over him and leave it...granted, Franklin was NOT afraid of being underneath things at all....this did not install any fear, but it gave him a "time out" and when he was ready, he'd climb out from under the cover and he was a whole new bird. Sometimes he'd stay under the cover for a few seconds, sometimes a few minutes, but always when he came out his attention was redirected from biting. This technique worked wonders for Franklin and it's also been over a year and he does not bite when he's out playing. We don't give him toys that we know will cause him to get over excited, like cat balls with bells inside...he loves them and on HIS time, it's okay, but on OUR Time...they aren't allowed.
We can't imagine life without or Franklin, he's such a dear...I don't think you are past the point of no return with your conure...but it's going to take some work. If you are definitely "checked out" of this relationship, then rehoming is your best option, but if you think you have it in you to give it a couple more months and try a couple new approaches, then you might develop one of the most rewarding friendships of all time.
As for the screaming, I think it's falling hand in hand with the frustration of not having a rewarding relationship with you. I think your conure is feeling the same frustration with communicating with you as you are with him.
I know that covering Franklin's cage when he'd try screaming non stop, curbed him from screaming. We allow a little bit of occasional screaming, birds just have to flock call sometimes - usually we can curb it now by just talking to him, he does talk with a pretty decent vocabulary for a conure, if he keeps up after a reasonable period of time, we will cover his cage and he stops and uncover it a short time later.
Let us know if or what you try and if you have any success if you decide to keep him a bit longer. He's 9 months old...and I really believe between 9 and 12 months are the most difficult after that, it SHOULD get easier.
Take care and good luck!
Toni