You are correct that most Orthodox Christians would not be comfortable with the Divine Liturgy of the Book of Common Prayer. When the Anglicans and Orthodox were discussing a closer relationship early in the 20th century, Orthodox leaders insisted that the BCP epiclesis was far too vague and weak. The Episcopal Church is essentially Protestant, but as one reader has written, enjoys processions and dressing up as if it were in the catholic tradition.
Thomas Cranmer, the architect of the Book of Common Prayer, incorporated elements of the older liturgies that he felt corrected flaws of the medieval Roman Mass. Cranmer's liturgy hardly survives in the 1979 prayer book because the liberals in the Episcopal Church didn't like the penitent tone that comes through from the Liturgy of St. Basil.
I enjoyed your interview. :)
Would you be able to shed some light on where the Anglican "Prayer of Humble Access" came from? I read somewhere that it had a predecessor in the Sarum Use, but have not been able to find out what the original was--at least in the Sarum texts I've consulted online. Or was it largely an invention of Cranmer's?