What I can understand from reading you is that your parakeets are not tamed and fear human contact. It should be known that the taming of parakeets requires an investment of time and patience on the part of his human, in a regular and motivated way. You have to listen to his parakeet and follow his rhythm. I think you went too fast and too "violently" in the training of your parakeets. I think you went too fast compared to the rhythm of your parakeets since you have to 'starve' them a whole day before they dare to come a little bit near you so as not to starve ... taming can last weeks or months before they dare to approach you. To have parakeets requires a real work of patience if one wants to obtain good results based on the confidence and not on the deprivation of food.
The parakeets (and also for many other animals) must have a time of adaptation to their new environment. (especially if you've changed cage for a short period of time, it's even more stressful to the bird, it takes them all the more time, but it's a good choice to give them a bigger cage ). The time of adaptation can be quite long if they come from a pet shop (because of the rough of the pet shop, passages of person, ...) moreover they are not very young which can also lengthen the time of adaptation to their new owner.
First, what can hinder the domestication of a parakeet is the wrong choice of the place of his cage. Place the cage in a quiet place with one side against the wall because having to watch the movement coming from all sides at once can make them nervous. For the same reason, avoid placing the cage near a door or a high traffic area. From what I can see on your photo the cage looks to be well placed.
What could increase the fear in your bird and complicate his taming, is to take the bird against his will. It could create fear. And he will be afraid to be seized at any time when you are near him. I do not want to deprive them of food. Because the bonds of confidence are created in abundance and not in deprivation, according to my opinion.
To tame a parakeet will require patience and perseverance but also the consistency and diligence! To start your taming well, it is important to always talk calmly and quietly and always have calm and controlled gestures when you are in the same room so they can associate you with some things of calm and confidence. Spend a few times near the cage talking softly with a warm voice (a sharp voice awake their attention). When you go, do not put your fingers in the cage, or between the bars, it's an invasion of home, his cage must be a place where he feels safe. From the moment he is no longer distraught when you approach, talk to him gently giving him millet through the bars at first. They need to associate your visit with some nice things (and not intrusion and stress).
Once these first steps have been put in place, and your passage near their cage is no longer a source of stress, then you can proceed to the second step. With a hand holding millet, you can put it near him in his cage (if he gets out of you do not try to follow him, wait for him to come to you). If he is not comfortable, a good trick is to look away always keeping your hand with millet in his cage, without moving. (The bird being a prey, it can be uncomfortable when it is watched with attention). Several attempts may be necessary for several days before being able to touch it. When they seem accustomed to millet (even if they do not devour it with voracity) you can try without millet, approaching your hand gently. Stop when he walks away and start moving again when he stops. Once you have managed to get close enough to him you can slowly start to touch his belly (no more than 2/3 seconds to start) and then withdraw your hand slowly. And repeat it several times a day over several days. They will see that your visitors in the cage are not dangerous.
Once the bird is on the finger:
Do not go too far from where the bird was perched (cage, perch, playground);
Keep the parakeet on your finger for a few seconds then let it go down to return to the perch or cage;
Repeatedly exercise the bird on the finger and place it where it feels safe.
To speak gently to the parakeet, it is necessary to congratulate it every time it goes up on the finger.
The first attempts, the bird will probably rush on his perch or on the cage. Then you should notice that the bird is climbing faster on the finger and may even stay there longer before trying to leave.
It is a paying exercise, because it proves to the bird that he can trust you. He will understand that when he comes to you, he can always go back to his house or to a playground he likes.
One must never attempt, in any way, to compel a parakeet to stay on one's shoulders, it must feel that it has the freedom to come and leave when it sees fit.
Little trick, the back of the hand is more reassuring than the palm. So you can start by presenting your fist as a first approach.
Courage for your taming. sometimes you can get discouraged because of the slow progress but with a lot of patience you will be happy with the result!
