I don't like calling the GOC "Chrysostomites," but I thought it only fair in this case, since the other name was "Matthewites". I'd like to post a strange, crazy theory here, and perhaps someone can tell me why it would never work. (at the very least maybe we can all learn a bit more about the various churches).
It seems that the Matthewites won't simply acknowledge the hierarchy of the GOC, because of how that hierarchy became bishops to begin with (ROCOR Bishops--including a Bishop who had New Calendar parishes under him--making the candidates bishops in a somewhat secret fashion, after which the ROCOR synod would not voice approval of the consecrations for a time). And, of course, Archbp. Chrysostom and his bishops are not about to claim that they were never bishops, or that the original consecrations were uncanonical. So what can be done?
I think that both groups need to forgive and forget (I can't believe I just said that!) What I mean is, there are lots of examples from history where a bishop had questionable origins. Pat. Meletios of Antioch, for instance, was placed in the Antiochian See by heretics. Afterwards, he affirmed Orthodoxy, and so some accepted him as Orthodox (Sts. Gregory the Theologian, Gregory of Nyssa, Basil the Great, etc.), while others did not accept him (St. Athanasius, the Church at Rome).
In the end, from an Orthodox perspective, I think it is safe to say that Meletios was accepted as a legitimate hierarch. He even presided over some sessions of the 2nd Ecumenical Council (and would have presided over the entire Council, except that he died). It is true that some did not go along with what was happening, but then some (e.g., Rome) didn't accept the 2nd Ecumenical Council either, and were not in communion with Saints like Gregory the Theologian. The point is, the Church (and a good many Saints) accepted Meletios, in spite of his seemingly uncanonical (as a point of fact, plainly heretical) origins.
Here's how I think this could be applied to today. The Matthewites and Chrysostomites could both acknowledge the validity of the other Church: that each hade legitimate bishops today, that each held to an Orthodox faith today, that each followed the canons today, and that each had sacramental and virtuous grace today. This is not to say that past transgressions are unimportant: it is only to say that love and peace in the Church is more important when two Churches have the same faith, the same sacraments, and the same Lord.
