AIY, gavra did not dismiss her discomfort (nor should it be dismissed, as you correctly point out that tznius is indeed a factor, as R’ Moshe says as well).
He dismissed her comfort overriding halachah, which is what these people want. They are not discussing, b’timimus, if there is a legitimate workaround. R’ Moshe did that already, and dismissed it as invalid.
You continue to connect this to a different, horrible story, but that was an issue of who ran the mikva, not who was on the beis din overseeing geirus.