And yet the EO still clings to the Byzantine Text in the Gospels, ala Codex A, and when Challoner revised the Douay-Rheims for the RCC, he made it read more like the King James with all of its Byzantine text, and every time those Alexandrian text type bibles are revised, they add more Byzantine readings because they know that they are the correct ones.
And all those great Greek scholars and scribes from Lucian of Antioch forward were reproducing Byzantine/Antiochian text type manuscripts not Alexandrian type texts. Those Alexandrian type texts sat on shelves like Vaticanus and were dumped in waste baskets like Siniaticus, but the Byzantine texts were used to make the Old Latin that the West used before Jerome, and the Syrian Bible, and the Lectionaries which the EO read from in their services, and all those cursive miniscules that dominate the extant manuscript tradition of the East.
It appears to even the unlearned that the Tradition of the EO was the Byzantine Text and that Tradition is maintained in the King James Bible.
Codex A is not pure Byzantine-type text. After the Gospels, it is mostly Alexnadrian-type. But you are correct in that the EO favored and still favor the Byzantine-type text, and that the KJV is an extension of that tradition, although far from a pure reproduction of the same.
As I mentioned earlier, no Church will ever admit to being wrong.