If I remember TKJ well, the assumption was that there was no red hood at all - the henchmen hired different people for each heist.
However, that's not my point. When I read TKJ for the first time, what I got is that the story about the failed comedian was taking place simultaneously with the Gordon subplot. As in - the Joker and the failed comedian are two different people and at the end the failed comedian becomes a second Joker; meanwhile, the first Joker fights Batman.
Again, I was very young and my firs copy of TKJ was in French, so...