So according to Kh. Krista West (from her Opinionated Tailor podcast: http://www.ancientfaith.com/podcasts/kwtailor/the_big_black_dress
), the exorasson is identical to the robe worn by magistrates in the Ottoman Empire, and therefore was likely introduced between 1453 and 1600 as a consequence of Ottoman rule. This would explain it, and might also explain why the OOs have it as well, since the Syrians, Armenians, and Copts were all under the Sultan as well. The Ethiopian Orthodox have it too, though, but it's not unreasonable to guess that they borrowed it from the Copts.