Wow,
Have you guys actually talked to any of these converts, or are you just spouting off? I personally know several converts to EO - from Baptist, Reformed, and Lutheran backgrounds.
On a social level, the answer is fairly obvious. EO has had virtually no presence in the USA until recent decades. They've just now gotten together some seminaries, a publishing house, and some network, so their influence is just now being felt.
But we're probably talking mostly about personal justifications. Here are some reasons I've heard:
1. Unity - converts to EO generally believe in the ideal of a single church, but don't buy the arguments for papal supremacy
2. Historical Liturgy - Many EO churches still have rites demonstrably similar to ancient (3-5 cent.) rites, thus reinforcing the idea of doctrinal continuity
3. Aesthetic Liturgy - Many converts to EO vigorously deny the "spiritualism" of Calvinism, asserting on incarnational grounds that the material is the proper channel for mediating the spiritual; they see Protestant (Calvinist) worship as bypassing the material and as being overly logo-centric
4. Anthropology/Soteriology - Many converts to EO see the West as being preoccupied with theories of original sin, merit, and consequently justification, and believe that their system of deification manages to avoid this; you might say that the East rejects both sides of the Augustine/Pelagian controversy
Lutherans seem to be getting hit particularly hard. I was talking to a Lutheran to EO convert and he said that at least 12 of his colleagues from seminary (LCMS) went East. Part of this may have been because of a surge of scholarship connecting Luther to certain Greek patristic theologians.
I think postmodernism is way off the mark as an explanation. Many EO's view postmodernity as being a Western problem. Catholics have a history of blaming Protestants for modernism, and the EO's have co-opted that line of argumentation to blame the whole West for the whole mess. Even some Westerners agree. The late Colin Gunton articulated this; see his The One, The Three, and the Many: God, Creation, and the Culture of Modernity. A recent work by an evangelical critiquing this narrative is Bradley Green, Colin Gunton and the Failure of Augustine. I have a published book review in Augustinian Studies.
I think this is accurate. Many that convert to EO do so because of the supposed history, liturgy, church order, mystical elements, theosis, etc. However, much of this can be said for Roman Catholicism. I think what differentiates the EOC from the RCC is the fact that the EOC has remained mainly in the East. As Westerner's look over, they are attracted to the different aspects that the EOC offer over the RCC and Protestantism. Also, the EOC has a different past compared to the RCC. There were no big crusades, there wasn't as much abuse as in the RCC, and for the most part, the EOC was being persecuted as opposed to persecuting others. The ones who are looking for the "ancient church", thinking it's the EOC or RCC, will choose the EOC for the reasons mentioned above.