Soy, you forgot a very important part of the Hawkman confusion; the Thanagarian impostor.
DC said that the Hawkman from the silver age JLA was Carter Hall... but the one from JLI couldn't be him, since he was fighting Ragnarok with the rest of the JSA at the time. So, they said that that Hawkman was an inpostor posing as Carter Hall.
Personally, I've never read an issue of any Hawkman comic, but I like this continuity confusion thing so I've read about it.
Dave, I'm not much of a The Bat-Man fan either, but there's some stuff you just can't avoid. My whole The Bat-Man collection is: DKR, Year One, Year Two, Killing Joke, Arkham Asylum and Long Halloween. I recommend all of those.
