Quote: My XW purposefully turned with a smile and made eye contact with me.
How is this a negative? Is it possible that you misread a limited reaching out by her to acknowledge you in a public place? What if you had smiled back in a relaxed manner and nodded your head or briefly waved?
Also, when was your letter to her? Are you referring to the 1 letter you wrote near the Christmas holiday season? Lots of time has past, and so she may have changed somewhat in attitude. I'm worried that your distant interpretations may be of your own creation rather than from her and your R reality.
When was the last time you've dipped your toe into the water, so to speak?
Forgive me if I am wrong, but I read a lot of resentment and judgment in your posts regarding your XW. What would it hurt to let that go and try once without that present to trip you up?