Hey and welcome to BB! Sometimes it helps to offer birds treats from your hands, be it while in their cage or with you... offer them a little treat that they will love! This often helps birds overcome their fear of hands and gets them more comfortable being around humans.
I say this because my budgies range in age from at least 3yrs to 8yrs if not a tad older. They are all flighted, and none of been tamed... however, in March, I decided to see if I could interact with them in some way... so I started out each morning sitting next to their cage, before giving them their morning food. At the time, they were all in a flight cage with a perch near the door. I sat next to the cage, with a hand full of seed, and rested my hand just inside the cage so that they could get to my hand from the perch, or from the cage bars. Gradually, they learned to eat from my hand without much fear, and even became somewhat eager over the best positions. Eventually, they came to a point that they trusted me enough that I could stand a few feet away from the cage, they would fly out, and onto my hands, eat their fill, squabble over the food, and fly about the room. I got them back into the cage mainly by giving them their morning food.
Now however, all are cage-free in the 11' x 14' room. They will still fly to me if I either have food or treats (i.e. millet) within my hands. Even though they aren't tame, I bet they could be without having to be clipped!
You might benefit similarly if you can get your GC used to your hands in such a way that he/she does not feel threatened.