I feel like we have answered this several times so I am going to flip it on you and ask what are the advantages of going to MC when the WW is clearly not working on the marriage?
I think one of your problems is you get to caught up in anything you view as a positive sign from your W. Your suggested MC so you viewed that as a positive sign when clearly so far it is not the case. When your W claimed she was upset she didn't get a letter you were never able to let that go as just another thing for her to complain about.
You have to try to get to a place where you say this is BS. I'm done. I am a great father, I am a great human being. Did I make mistakes? Sure did because I'm fuching human. If you want to actively work on the marriage then I will continue with MC. If not then I'm not attending anymore. Take some time and let me know.