You understand Bayes' Theorem. You enter into a situation with an intuitive "common sense" prior. You observe the situation, and then you shut up and multiply.
And then you go to update, you compute the desired behavior to maximize utility... and some cognitive module buried in your brain says "no".
Example:
I realize I need a physical examination. I have no rational reason to fear going to the doctor. I am, in fact, acutely aware that my fear of going to the doctor is based on a fear that they will find something wrong that I can't afford to fix, but the truth is already so. So I bite the bullet, make an appointment, and then at the scheduled time I get in the car and drive to the doctor's office.
And then I just keep driving past the doctor's office, turn around and go home.
I tell myself that if I'm not going, I should call the doctor to avoid a $100 no-show fee, but I don't.
And then I get home, and I tell myself that that was dumb, and that I need to update my behavior - and that physically punishing myself for not going to the doctor is not an efficient use of my energy.
So I punch my hand through a mirror.
NOW, finally, I have an excuse to go to the doctor - so I wrap my hand in bandages and go back to bed, instead.
What do you do when your computed probabilities and utility function have NO EFFECT WHATSOEVER on your actual behavior?
... it's hard for me to imagine what you've been through. I'm sorry.
When you say that you operate under this belief system, I don't quite believe you. You don't seem to identify with it. Maybe you've updated out of it in some regards but not others? Maybe you apply it to the way you would let others treat you / how you treat yourself, but not to the way you treat others?
Also, I'm going to guess that you're still punishing yourself for your mistakes of the day. I hope you can let them go. You're obviously working through something painful. Have you given yourself credit for taking the bold step of making this post to try to find a way out?
As for your original question, the only approach I know of for failure, generally, is to try again the next day, possibly trying something different/smaller, possibly with help. Failure to act according to your "system 2"-intention happens to everyone, so I'd say the most important things are (1) not being to hard on yourself (2) setting things up for a new trial with a high success probability (3) recognizing small successes. E.g. set things up so you can avoid most of what your averse to, without completely avoiding all of it, and/or find ways to be less averse to it.
I hope this post isn't too off-base. I wish you well.