No amount of editing can catapult certain songs into radio-friendly chart toppers. There's just no way songs like Man of Action and Suburbia, though awesome songs, would ever fly as singles. This is a painfully obvious fact. It doesn't matter if Carmelina and Rico were not successful singles, they had the forumula that conventional singles follow. Every once in a while there will be a deviation, but in the case of the songs you're proposing should have been radio singles I just don't think so. Carmelina and Anti-Pop were the only things resembling radio singles on Audio of Being. Beautiful Midnight had perfect choices for singles. Maybe the choices for Underdog were a bit off base, but not terribly so.
As far as Hospital Music goes, anybody who suggests Champions of Nothing for a radio edit is just plain not thinking clearly.