I think being a Scholasticate graduate (as well as having battle experience) helps in becoming a member of the Heavens' Ward. I think it was said said that some Scholasticate graduates eventually become members of the Heavens' Ward.

Additionally, does each Archbishop personally select members (kinda like a president's Cabinet, etc) or are they assigned separately? I'd imagine that the Archbishop selects the members they want considering how close they are to each other