I understand your urge to remain in contact with him for fears that he might move on but right now, it would be better to give him some space to breathe while you spend this time making positive self-improvements and working on the issues that caused the relationship to fall apart. The constant fighting could have caused him to re-examine the decision to remain serious and committed to the relationship, especially if he wasn't happy anymore. You're going to have to identify the root cause of the fighting, and avoid taking the same steps again. If you still want to send the letter out, I think it would be fine but avoid contacting him before and after you send the letter out.
One of the most devastating mistakes you can make is trying to force it to work with a guy who is wrong with you. I’ve seen people spend years of their life trying to shove a square peg into a round hole. Everyone in their life tells them to just move on and let him go but they can’t. Why? Because they don’t have clarity or any objectivity because they are still sucked into the emotional whirlpool and have yet to break themselves free. <<<<