It is obvious that one would want to dialogue with the GOC of Chrysostomos II as the Church with its roots firmly in the Florinite tradition and which is by far the largest GOC. The Lamians are a dying off schism (just like the Gregorians)--on paper some of their claims look legitimate, but for heaven's sake two of their founders were Metropolitans Paisios and Vikentios, who went EP and were "reordained" after being "rechrismated"! Also note that out of the six bishops who formed the Lamian Synod, all but two left the next year for the Athanasian Synod (which fell apart, I believe all of its members either dying, returning to Chrysostomos II, or going to the EP), while the two left, Kallinikos and Euthemios, were divided amongst themselves until they reunited, made new bishops, and remade their Synod; in effect we should really call the Lamian Synod the "Lamian Synod, Part II."
I am afraid that it seems that the Auxentities are not even a GOC anymore after they began consecrating with a pseudo bishop from the Alexandrian patriarchate (I am not calling all bishops in the patriarchate pseudo; I am saying that it seems it really was a guy claiming to be a bishop who was never consecrated). In fact, it seems the Auxentians have split into three groups? Maximos, Auxentios II, and HOCNA? I am not totally sure about that though.
I think that Metropolitan Cyprian's Church is the most consistent and has the highest morals, but the cost to achieve that has been a very pervasive and watchful program from the top down. Reading the corpus of Orthodox Tradition back issues is sort of like that picture of Stalin with his friends, the one where a few years later one of the guys is missing, a year later another guy is missing, until finally it's only Stalin left because he killed off everyone else. The Cyprian group is much like this; an upandcoming and promising individual is lauded; a few years later, he is mentioned as having been deposed on the back page with one sentance and no explanation. Bp Auxentios has been most helpful to me personally when I have corresponded with him, but I do not think I could ever fit into their homogenous program. Despite that, I still highly respect them and must say that their literature had a decisive impact on my decision to become Orthodox and had an even more decisive impact on how I have come to see the traditional exposition of Orthodoxy. Thank God for them!
Yet the Synod of Chrysostomos II remains; despite the horrible events of 1995-1996, they are reunited for the most part; they are spreading in America with missions; etc etc etc. Clearly they are the "winners" if we can look at it that way. The "Matthewites" would do well to join together with them.
Anastasios