Actually, I posted a similar theory for book 7, not six, but I also had Harry invoke Ereshkigal at the climax of The Triangle Prophecy (http://www.schnoogle.com/authors/barb/TP01.html) (Harry's seventh year); he had to go to a realm of the dead that looked like Hogwarts, leaving different pieces of clothing behind him until he was naked (like Inanna). When he confronted Ereshkigal--she looked like Lily.