I think you've done well gaining perspective on what happened, and are approaching a difficult transition with a good attitude. If you feel sending the letter will give you more closure, I would definitely send it. I just want to mention sometimes when I send a message, thinking I do not want or need to receive a reply, sometimes, later, I change my mind and realize I really to want a reply, so, just something to consider in case that might happen with you.

Please take really good care of yourself, please be kind. Treat yourself to something you enjoy and do things that are comforting to you.