Avirah, I disagree with you on one thing.
You attempt to prove that the Vilna Gaon was definitely greater than the Baal Hatanya from Litvishe sources. I don’t see anything wrong with Lubavichers believing that the Baal Hatanya, who we all agree was an absolute giant in nigleh and nistar, was greater than the Vilna Gaon.
As an aside, i have heard a number of times that one of the early Belzer Rebbes said that the world thinks that the Vilna Gaon was greater than the Baal Hatanya in nigleh, while the latter was greater than the former in nistar. This is actually a mistake as the reverse is true.