I am really sorry that you are going through this.
You are probably overloaded with advice, but I watched my brother, my brother in law and a friend all go through something similar.
My advice is not very popular but it did work for the two who followed it. But it is a gamble and I wouldn't guarantee that it works.
Surrender.
It sounds counter intuitive, and it may be a little late for you to try. But this is what I told him.
My brother started down that path and I told him the first thing to do is face the fact that you may lose contact with your daughter. You really have to believe and be ready for that to happen. That way you are not playing chicken, you are really giving up. I don't know if you are a man of faith, but you have to put your daughter in Gods hands.
Then go to your ex and tell her as humbly as you can (Believing it is vital)that she has the power to take your daughter away from you. As much as you want and need to be in your daughters life, your ex has the power to take that away. So if she decides to do that, you can't afford to fight her. Tell her she won. But don't do it to manipulate her. Because if you don't believe you can lose your daughter and that she really does have the power to keep her from you, it won't work. It may not work anyway and you would have to be ready to face that.
No matter how much you drag her through court, it will make her reflexively fight back. Don't give her anything to fight. Every time you send her a summons it steels her resolve. Every time you try to force her to do something, she will instinctively resist. She has the advantage. She has had your daughter longer and she is her mother.
It is kind of like relationship judo. But you can't do it as a manipulation or a game.
Another thing is that every time you tell her you don't want to pay child support, the message will get to your daughter that fighting over money is more important than she is. Even though it is completely untrue.
You also have to stop blaming or hating your ex. It makes it all harder for you. She is what she is and you can't change that. Don't waste your energy on her. When you are angry with her, she is winning because she is controlling your emotions and draining your energy.
My niece is now in high school and spends whole summers with my brother. The relationship with the ex is at least amicable. She was even there when my Father passed away and nobody was upset by that. It was a little weird, but not painfully so.
I understand if you don't take the risk. Like I said, you have been at it for a while and your daughter is older than the people that I knew who went through this.
Regardless, my prayers are with you both. I hope at least that helps.
I want to go out like my Grandpa did. Peacefully in his sleep.
Not screaming in terror like his passengers.