Want Some Latin with Your Greek?
My first impulse is to go with the Greek -- I am trying to evoke the experience of living in the Greek Age of the Gods, which should not be filtered through Roman recensions. This means emphasizing some distinctions most English readers do not really know about, like the fact that the Latin ligature æ is a transliteration of the Greek letters "ai" and should be pronounced with a long a rather than a long e. (The Latin ligature that should be pronounced with the long e is œ, as in œconomia and fœtus.)
This doesn't bother me, and certainly most readers have encountered spellings like "Hephaistos" and "daimon." But "ph" is itself a Latin creation, for that sound is rendered in Greek as one letter, phi. If you transliterate that properly as "f," you get words like Hefaistos, Fobos, and fallus, which I don't think readers will accept.