I think the letters work once in a while. If you'll read Crimson's thread, you'll see that he just might get an opportunity to at least speak with his W before the D. Here's his last thread:
Here's the thing, Crimson has made a 180 in who he is as a man. He has faced things about himself that was very painful and he has changed what he had power to change and he's regretted what he messed up and now what he will miss. He knows that his M has probably ended and on the way to D court. He poured his heart out to his W in a letter, not begging her to take him back, but telling her she was right to be hurt. He spelled out the things he now sees that he didn't see when she was with him. He didn't just sum it up, but he took event after event and case after case where he screwed up. He talked about his behavior, his failings, his wrongs......not hers. He spoke from a pure heart of love and regret. It was what he wanted to leave with her.
Now, if he had tried this when his W first left, it would have fell on deaf ears, more than likely. But timing is everything. He had to grow, first. Hopefully, it has stirred her heart enough to listen to more. If not, then he is as prepared to move on as much as he possibly can be.
So, don't write a letter with intent of just apologizing. Not that you shouldn't apologize, but don't use it as a tool to pull her back. And, apologize for the new areas, as you stated, not something you've already apologized about. Don't try to win her back or beg for another chance. If you've done this already, then she's not going to hear you. She has to see real change. She wants you to tell her what you know you did wrong and what you've learned, and what you are doing differently. Otherwise, I don't think it will be enough to change her direction, but that's my opinion.
I agree about discussing it with your DB coach.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!