From what it seems, we have a little bit of time. But not enough to do any real sneaking in the way of finding the key and stuff. If we let ourselves get thrown out, we're pretty much going to have to storm the place or pull out the public speaking skills; and taming an angry mob is gonna be a hell of a trick.
Alternately, we could leave, hide, wait for the kangaroo court to begin, and do a dramatic reveal, and try to calm the crowd that way. It'd at least put them in a setting where they have to listen to us.