I don't think the ignore game works very well at all. He is part of your flock. It betrays his trust.
The bird is trying to communicate something to you. You are crossing a line and he bites because he doesn't know how else to clearly tell you NO! It is better to allow the bird the confidence to communicate. You need to work on reading his body language to know you aren't always going to push him to the limit.
If your bird doesn't want scritches or want to interact with you allow him that. He is growing up and will need less babying. Parrots communicate a lot with their beak.
Most of the time my parrotlet will touch his beak to my finger to push it away when he doesn't want scritches. I stop the session and let him go back to his thing. Sometimes he even freaks out at my finger, this is normal parrotlet dialogue. When he wants scritches again I give him that. Even if you see parrotlets communicating with each other, the beak is always part of the dialogue.
You should definitely keep playing with him and being affectionate, just slow down and take a step back if he is having too much. Birds have a lot of work to do daily, lots of foraging, eating, preening it is normal for him to need some independent time. If he is maturing he is also having many hormones and feelings to worry about. He is trying to find his own pace. None of this means he doesn't still love you. You are his flock and probably the most important part of his life. When you have ignored him when he tried to communicate that is a very upsetting thing. In his mind, he was telling you everything he needed to and he got abandoned for it.
If he has his own play stand and foraging area it would help to give him random rewards whilst he is there. Every time I walk by my birds I tell them how they are good boys and sometimes hand them a treat. It helps them understand how rewarding the play stand can be.
If he is pursing you to bite that can easily turn into a very bad situation for everyone. DO NOT cage him! This will not help him thrive or be a healthy bird. My advice is to try and respect his body language more. He might be finding you threatening. If he is spending lots of time in the cage he may also be more cage territorial.
Try googling more videos of linnie body language. Study it. You need to master the communication and take a step back. You need to reestablish trust.
@Dona has a linnie named Gigi. Maybe she can help you with body language resources for linnies.