I'm going to agree with some of the comments about your letter. Something I did that helped me is writing a letter about what I really wanted to say to my XW. Then I sat on my patio, had a drink and burned it.
Actually what did happen with time is that I waited to get emails from her asking how I was. This took a good year to happen and would happen when I had stayed in NC. She would say how much I seem to be flourishing and how happy I seem. She also mentioned having to pay for her sins and how karma is a bi%@#.
Be careful about this letter. It might seem like pursuing and it make you look weak. Let her intiate the discussion. Trust me, she will think of you.
I would not say your approach is a failure either. I would say you must be patient and back off, and move on. Planting a seed of doubt takes time to grow.
Formerly SGfan M:38 W:33 M:8 yrs T:10 yrs Bomb: Dec '08 Separated: 4/18/09 Divorce: 8/28/09 XW Affair began: April 08