I think your letter was heartfelt and honest. I sent a similar one to my H after out last tiff, and got no response at all. I don't even know if he got to read it, as I suspect OW censors his mail.
At least you know that he was sorry for the way things went, as well, and was even quicker on the draw to write than you. Great minds think alike, I always say. Sometimes it takes a blow up to clear the air, or clear the clouds in our/their minds for a moment.