Well thanks! I don't know exactly what I did, but apparently I must have met all of the requirements because talking to the green haired guy at the "secret base" progressed me through the game.
I got into the casino, got through the VIP room at the back, and finished fighting all of the monsters there. Now, I'm stuck again at a portion where I cannot leave the hidden area in the secret base, and my only option was to go back to the casino through the hidden tunnel. Once there, I broke the jail doors that were holding all the monsters captive, spoke to all the monsters, and now again, there's nothing to do...
I even went back to the secret base and spoke to all the NPCs there again, and then back to the casino, again. Still nothing. I cannot leave either building.
I may have also found a glitch:
During this stage of the game where the casino is essentially empty, if you go back into the VIP room (on your way to the arena), there is a glitched door on the right side of the admission room. The door can be opened, but nothing happens, and the area behind the door is blocked by the wall anyway.