Forgive me, but the claim from the Watchtower that the earliest LXX copies used various forms of the Tetragrammaton is quite false. Second generation fragments have been discovered with it, but originally the LXX had nothing where the Divine Name occurs in the Hebrew.
Papyrus Rylands 458 is the oldest fragment of the LXX. It does not use contain the Divine Name. Instead there are blank spaces, often with a dot. The second generation fragments appear to come next but the practice seems to have been discarded in favor of the substitution.
While the Tetragrammaton is special, it us because we Jews don't see it as a "name" as such. In our culture it is viewed as an "anti-name" or the opposite of a SHEM, a "handle" for which to manage or control one. Some Jews utter "HaShem" when coming across the Four Letters, meaning "THE Name," with the emphasis on the "Ha" or "the," because it is a "name" unlike any other.
The use of it in the LXX was experimental, as its sudden appearance after Pr458 demonstrates. The LXX composers were not sure how to handle it, even employing the very old, long unused Paleo-Hebrew for a while before abandoning it altogether.
And it wasn't left unpronounced because it was "unique," but because it was "holy."
In Jewish theology, holy things are left untouched or at least used less than the mundane, everyday things of life . For instance, the Holy of Holies was rarely entered, and then by only one person each year. The Ten Commandments were hidden from sight in the Ark, and the Ark itself was hidden in the Holy of Holies. If you touched it, like Uzzah did, you would die. (2 Samuel 6:6, 7) The consecrated bread on display was not to be eaten until it had remained before the entrance to the Holy of Holies for a specific amount of time, and then when it could be eaten, only the priests could do so. That is why it was a big thing for David and his men to be offered and eat this bread when they were hungry. It was not for mundane use. (1 Samuel 21:5, 6) And it is the reason Eve adds the injunction not to "touch" the fruit of God's tree when God had only command that it not be eaten, since the Hebrew custom is that the holier something is, the less it is to be used or ever.--Compare Genesis 2:17 to 3:3.
Since the Tetragrammaton is God's Self-Designation beyond the scope of common names, and because it is God's Name, it is like the fruit of the tree, the Ark, the Ten Commandments, the Holy of Holies. If something is to be "hallowed" in Jewish custom, it is not to be used. It can be there for all to see, like the fruit, the Temple that housed the Holy of Holies and the Ark, and even the eating of the presentation bread by the priests, but it is not for common use. That is something more than unique, like the appearance of the Super Moon we are witnessing in the night skies right now. What is unique is more mundane than what is holy.
Pagans repeatedly uttered their divine names to show that these names were unique, special, and even holy to them. Jews did the opposite. The holier something was, the more purposefully far removed it was from use. This is something that might escape a Gentile audience since the culture of Hebrews is not well-understood outside our own people, and Christians are more often to side with their own scholars and teachers over our own Jewish history and experience (as one Christian once told me upon learning I was Jewish: "What do Jews know about the BIble anyway?"), but it is not the good use of critical thought to ignore it.
And by the way, Papyrus Rylands 458 is not from the 3rd century or Christian, as you stated. It dates to the 2nd century BCE and is Jewish.