Just a few minor corrections, because I know you are paraphrasing but the Eastern and Oriental Orthodox absolutely do believe in the canonical teaching authority of the legitimate hierarchy and part of the "schism" is how hard they hold onto certain authoritative definitions. The problem is that, and I don't see a way around it, without the papacy, they've effectively lost the ability to hold more ecumenical councils to define dogmas and anathematize errors. The loss of papacy in some ways appears to equate not only to a loss of the Apostolic teaching office, but even to truly be a communal Church, in that they have all these asymmetrical communions and excommunications without any mechanism to resolve them. We're in the middle of one right now with the Greco-Russian schism, where Russian Orthodox are discouraged from attending Greek Orthodox sacraments, the other side deems the inverse as okay, and the rest of the ethno-national jurisdictions are left to decide how best to make heads or tails of it. What's more, this episode started because the Ecumenical Patriarch unilaterally exercised the universal jurisdiction which he and his bishops claim does not exist.