So I fought the Mongolian herd on the top of the tower. I took the exit and it brought me one level down. But there's no exit down from that level?! Is it because I already set off all the fireworks before I went up?
So I guess you already figured it out but for all the other players having the same problem:
The exit is on the far left of this platform behind the pillar
The original questioner figured out his own question, and edited his answer into his question.
The apparent solution was roughly:
The barrel is on the left hand balcony. I just didn't remember where it was and behind the barrel is easy to miss.