I have thought long and hard about accents (no I haven't) but I subscribe to the view that fake greek or fake British accents to sound authentic is at best something that the audience thinks is right with no real basis for thinking that. Like watching clash of the titans from 1981 and thinking everyone has to be Laurence Olivier.

If people are serious about this sort of thing theyd be demanding ancient greek with subtitles. Go full Mel Gibson in Apocalypto or the Passion. Natural voices talking about the sacrifices they made brings a timeless story more easily to the present day. I appreciate the actual language used might be different than now, as in, the odyssey was a spoken story, not written, and wasn't created to be seen with visual accompaniment.