You are being irrational right now because you are out of options. You are dying to pursue (even though we have told you it never works), Just do it and get it over with and send him the letter apologizing for everything humanly possible you did in the relationship.
If you need to pour your heart out and explain your eternal and unconditional love for him in order to feel you left no stone unturned and to get closure, then you should do it.
Before you do it, I would just ask you to consider what will happen if you write the best letter of your life, one that would make anyone who reads it tear up over the sheer beauty of the language. What if you write that letter, he reads it, and nothing changes.
What are you going to do then?
Is there any chance that you will then feel you didn't express yourself clearly enough, and need to write another letter?
I guess what I'm asking is "where is the finish line?" At what point do you feel you will trust that he fully understands how you feel and still chooses not to reconcile?
I hate to ask you that question, but I also don't want to see you forever stuck.
If you pour your heart out and nothing changes, what comes next? There is nothing you can do right now to end the affair or get your H back.
How does that feel? Crappy right? Used to fixing things? Used to finding a way? Familiar with the feeling that if you work hard enough, anything is possible? None of that applies now, there is nothing you can do. You need to surrender to that, grieve it and find peace with it. Fighting against it sets you up as their adversary, pushes them together and you away. If you continue to actively try to disrupt the affair and get your H back, you will only dig your hole deeper and deeper, and that will be a debt that will take you a long time to recover from.