Perhaps you dislike the tension between the much more closed ecclesiology of Eastern Orthodoxy and the ecumenism in some EO circles that belies that ecclesiology?
Actually, I believe and support the Eastern Orthodox position as it is clear that they have every right to it. When individuals ask me about the Orthodox Church, I am generally given the old line: "But wasn't the Church Roman Catholic before the Schism?" I always answer, "No, the Church was Orthodox." I realize you are Catholic and therefore hold the opposite opinion, but that is my mind, at least. Generally, the Catholics and Orthodox seem to respect each other's claims to being the One Church, though they profoundly disagree. The Protestants were the ones who seemed to flip out when the CDF (I believe) issued their statement repeating this classical RC ecclesiological opinion--the Orthodox did not seem to have so vocal a response.
As such, I do not particularly subscribe to the "Branch Theory." The Church is one. However, it is my opinion that the Anglicans have and can make positive moves towards Orthodoxy. In fact, I believe that knowingly or not, that was what the Reformers in England were doing from the start--if a group tries to remove baggage that's built up after the Great Schism, it will ultimately find itself seeking the Orthodox Church. The Non-jurors certainly seemed to realize this, as did Bishop Grafton in this country in the early part of the 20th century. Ultimately, I believe that the vocation of the Anglican Church lies within Orthodoxy, though I do not see this provided for in the Western Rite (which someone might posit.)