I don't see how "Blue Dahlia" would ever work as a closer. It's a great song, but doesn't feel final at all, and would leave the record feeling incomplete. If you're going to close it off in "big" fashion, you need a song like "The Backseat," and there's nothing like that here. "National Anthem" fits with the direction they take in the last three songs.
"Blue Dahlia" is definitely the "biggest" song they recorded for this record.. if it were the closer, I agree in that I dont' think "Mae" would work as second to last, though.
Good thing we don't live in the days of b-sides never seeing the light of day, eh?