"Exapostilarion" is how it is spelled in Bishop Kallistos' texts. It is also spelled this way in the Boston texts, Fr. Ephrem Lash's translations, and in the Menaion and Octoechos by St. John of Kronstadt Press.
Exapostilaria beats Exaposteilaria by 535:340
Wikipedia also has it's article spelled this way:
Both transliterations are defensible, but I think the "exapostilarion" transliteration is the one found in the best examples of Orthodox English translations.
Frjohnwhiteford 15:45, April 15, 2007 (PDT)