Welcome to the forum! I am sorry to say that you have a couple of problems that are causing the bird to scream. For one thing, ignoring the screams of a baby bird is actually the opposite of what you need to do for a bird not to become a screamer when adult. I don't know where you got that advice from but it was the wrong one and the main reason why your bird now screams all the time, even when he is on you. I know that it seems logical to think that if you ignore an undesirable behavior, the animal will realize this and, in time, stop the behavior completely but that is ONLY when the behavior is an abnormal one which is not the case with a baby bird screaming for attention. That is like saying that a baby that wakes up from a nap and finds himself all alone in a room and cries for attention is doing something wrong or abnormal and should be ignored - quite the contrary! It is the most natural and normal behavior for a baby to cry when alone because being alone is scary and dangerous, and going to the baby and comforting it is the right thing to do. When you ignored your baby birds screams, what you actually did was to teach him that even though he needed comfort and company, you did not care. I know this is not what you were trying to do and I am sure that you did it thinking it was the right thing to do but it wasn't, it just made the bird insecure and anxious and even more needy than a normal GCC-and that's saying A LOT!
See, the thing with parrots is that, to them, having company [and, to a baby parrot this means being ON you, with its body touching yours and feeling the warmth your body emits] is not a luxury or something they just like, it's something they NEED and, when they don't have it, it does something to their heads, the same way that a human baby that is left alone most of the time grows up with psychological issues. Parrots evolved to be always surrounded by their family, from birth to death, and GCCs are extremely needy about this - even more so than other species. The need for company is hardwired into their brains, it provides a sense of security, of safety, of belonging... it gives them a feeling of wellbeing.
The other problem you have is that he doesn't spend anywhere near enough time out of cage or on a one-on-one. The rule of thumb for parrots is four hours out of cage and 2 hours of one on one but GCCs need much more than that. It's just the way this species is...
Then you have your system of 'disciplining' him. The putting him in his cage when he screams is not the way to go. It works for dogs and children but not for parrots and I'll tell you why. Parrots don't understand the concept of obedience or discipline because they don't belong to hierarchical societies so there is no alpha, no leader role they need to follow or obey. Every bird is the same in a flock and they all make decisions on their own so trying to impose our will on them is not only futile but completely counterproductive. Now, I am not saying that I have not used this method because I have and, most likely, I will again but I only use it when a parrot attacks me or another parrot and the 'time-out' is never longer than a couple of minutes because the purpose is not so much to punish but to distract and/or redirect.
Now, as to how to correct the situation. Well, the very first thing you need to do is to make sure that he is kept at a super strict solar schedule with full exposure to dawn and dusk [at least, 1 hour each] and that he is kept at a low protein diet [which means no free-feeding ANY type of protein food like pellets, seeds, nuts, etc.] - these two measures are to make sure his endocrine system is kept healthy and in tune with the seasons which will, in turn, avoid his getting overly hormonal [a problem that makes them scream, bite, pluck, etc - please research avian photoperiodism, avian reproductive system and avian endocrine system for more details]. Then you will have to put up with his screams and go to him every single time he screams to comfort him PLUS give him, at least, 6 hours of out of cage time and, at the very least, 4 hours of one on one -which is what adult GCCs that have no bird mates need. The idea behind the 'comforting' him when he screams is to make him realize that he is not alone and that you do care so as to 'build him up' emotionally. This, plus a strict schedule with unchanging daily routines, will give him a sense of security and belonging which, in time, will make him stop screaming all the time. Mind you, this is not going to be solved overnight or any time in the near future! I had a cockatoo that was a screamer [he was left alone in his cage all day long while his owners worked] and it took me ten months of 'reassurance' and constant company [I not only don't work, I don't even go on vacations every year because of the birds!].
I now have only one GCC, a female named Codee, but I've had four altogether and all of them came to me because of bites and/or screams but they all did great once they were rehabilitated and they are all still doing great today in their new homes. Codee never screams or bites and she has the sweetest, sweetest temperament! I often joke that she is a kissing fool because first thing she does when she goes on my finger is quickly climb up my arm to reach my shoulder and kiss my cheek. If I kiss her head, she kisses my cheek. If I lower my chin so as to 'catch' her head under it, she kisses my cheek. If I say her name, she kisses my cheek. If I tell her 'I love you', she kisses my cheek. A veritable kissing fool!
Even my kids know about this as they hear the 'smack' she gives me when I am on the phone with them and would often ask: "Codee is on you, isn't she?" But Codee doesn't only spend a solid two hours on me every single morning, at the same exact time every day, she is kept at a strict solar schedule, fed a fresh food diet that changes with the seasons but also has a mate so she is never alone.
People see GCCs as 'easier' parrots because of their small size and loving nature but, in reality, they are harder to keep happy than larger species because they are much needier - so much so that I often compare them to cockatoos! And, if it's not easy keeping a larger parrot happy and healthy, it's much, much harder to do it with these little guys...
I don't know what your work situation is but, if you work full time outside the house, you might want to consider keeping him cage-free in a room of his own [and that means a room that has no human furniture] and getting him a mate but, if you do, don't get another baby, adopt an adult of the opposite gender because adult birds don't bond with non-adults and you might end up with two troubled birds instead of just one.