Bishops sit on the thrones of the Apostles having been ordained through their ministry to power and authority given to them as overseers and leaders of the flock. Bishops are the image of the Apostles in this world and continue their ministry to guard the truths, protect the faithful and feed the flock. How? By the Holy Spirit.
Even if all that were true, none of it makes bishops in general, nor Ignatius in particular, apostles. Ignatius was not an apostle. He himself said so.
No they don't have such a list because there are many considered so and many not even known.
Do you have any way of knowing if any given writing was divinely inspired (i.e. God breathed)?
And, once again, can you show me a source that speaks in any kind of authoritative way for the EOC, saying that the EOC teaches that some writings outside the Bible were divinely inspired?
I am not the only one claiming that. That is the teaching of the Church. The Bishops have continued the apostolic ministry initiated by the original twelve.
Even if that's true, continuing the apostolic ministry doesn't make them apostles.
Later Church Fathers revealed it, the Church has proclaimed it
Some later human beings claimed it, and others believed them. But "the Church" never said anything about the matter.
It was already a given being that he was appointed by the Apostles (namely St. Peter) to take over the episcopal duties after St. Evdovius passed in 69AD.
It's not a given, because everything after the words "being that" is just some legend that you heard from some human being. Do you have any evidence for that claim?
Peter died in AD 64. Why do you think he would appoint someone to replace Evdovius, if Evdovius was 5 years away from dying? How could Evdovius have been the bishop of Antioch prior to AD 69 when monarchical bishops didn't even exist yet in AD 69? And how old was Ignatius in AD 64 when Peter appointed him to take over a bishopric 5 years off into the future?
It is not just a human being saying so, it it the communion of baptized Christians inspired and guided by the Holy Spirit which make up the Church which tell you so.
That's provably false. Every member of the community of baptized Christians is made is a human being. The Holy Spirit baptizes, indwells, seals, convicts, and enlightens, each and every one of them. And some of these human beings say what you believe, while others don't. This has been the case throughout the entire history of the Church, from the first moment when your beliefs came into existence--some of the human beings said what you believe, and others didn't. You seem to arbitrarily pick whichever human beings you happen to agree with and say that they're the ones guided by the Holy Spirit, so they must be right. How do we know? Because they agree with TER. No appeal to the opinions of the apostles as expressed in their own writings is necessary or helpful.