All those Latin Vulgates floating around are sufficient proof — but of course that may be Greek to you.
All those Latin Vulgates floating around are not proof that Greek Orthodox priests and monks were the ones who were copying the New Testament over and over for centuries.
From the time Jerome translated the Vulgate to the time Gutenberg printed his first Bible (again, a Vulgate)--roughly 1050 years--you are claiming that it was Greek Orthodox monks who did all the recopying and preservation of the New Testament?