These are always such stupid tropes. Go to a party in...disguise (I guess it worked for Clark Kent) to uncover a crime which is already on full display. No don't do anything, it might blow our cover. Voluntarily separates from allies then act surprised when the extortion occurs.
At this point just break everyone's legs while your thief locates the documents. Now no one can run, the evidence is secured, and there's no fatalities.
Oh and let's not forget it's not the slavery that's illegal, even the sex aspect is legal, after all the hero did this very thing in the first chapter. Even the battery can be chalked up to discipline under their laws. It's just the rumors of torture and killing of slaves that made this something to be investigated. So zero reason not to just start throwing hands.