Let some time go by before you send it. Personally, I would not send it. She is done with the M. LRT! The letter sounds like you are begging for a second chance. No begging. It doesn't work.
The S you are sending it to is not your W right now. She is not the woman you married.
LRT and GAL. I am so very sorry that you are where you are right now. I can only imagine how hurt you must be feeling right now.
Start working on getting on with your life without her. If she comes back, that would be great. But for now, go out with your friends and find your happiness. You deserve some happiness after the work you have put into your R.
My prayers are with you. Keep posting on your progress.