We read your original post thoroughly and all the other 27 pages of posts. We looked at your beautiful coop and run. We live in NH, and we have a run with a 'roof' of the same clear corrugated plastic that yours has. We agree with everyone here who advises you to FIGHT THIS. Before we would ever remove our run roof, we would fight this all the way. The folks here who said that your plans were approved long ago, that you were grandfathered in and that the neighbor moved in AFTER that when the coop and run were already in place are correct.
We truly believe you would win any legal battle regarding this. As advised by others here, we agree and also advise you to leave the roof on, and consult a lawyer. A first consultation could be free and you would be advised on what kind of a letter to write. We would first go get a copy of ALL the laws/ordinances, and highlight every single thing applicable. Then consult an attorney. We truly think the guy doesn't have a leg to stand on. Additionally the commissioner is NOT "compromising"---He is going back on what he told you and approved years before, and now asking you to change what he sanctioned to MAKE THINGS CONVENIENT FOR HIM, and a PITA neighbor go away! This is ridiculous! There IS a precedent here, and your 'run roof' is NOT illegal or against any town ordinance! PLEASE fight this for all chicken lovers. If you cave on this, there will only be something else. It will never end, because THE PROBLEM IS NOT YOUR COOP OR RUN OR EVEN CHICKENS. THE PROBLEM IS AN UNHAPPY INDIVIDUAL WHO HAPPENS TO LIVE NEXTDOOR, AND WHO'S LIFE MISSION IT IS TO MAKE CONTINUAL TROUBLE IN ONE FORM OR ANOTHER, FOR OTHERS.
I would fight to keep my coop and run exactly as I designed it, as it was approved, and constructed! This also sends a better message to the jerk neighbor, that you WILL STAND UP FOR YOUR RIGHTS and not back down. Please keep updating. We're all sending good wishes and hoping for a great outcome for you.