James, I am not so sure it is about giving up. I think it has to be about making different choices.
No contact is for you and you only. It is for you to get your life on a better path. What your W does during a period of no contact is not something you can control.
Your W is a deeply disturbed woman... proven by the website she is on and the terrible lie she told you regarding custody of her own child. You cannot "fix" those kinds of issues.
Take care of your health so you can get back to work and start rebuilding.