I don't know that we have much room to maneuver here, honestly. Hazou is the clan head and host, and is already on the back foot from Oro's surprise entry. If we just follow his lead and leave to talk in private, we'll not only be rude to all the other attendees, but we'll also establish ourselves as being easy to jerk around, both in Oro's eyes and everyone else's. We need Hazou to recover some poise, and that's easiest to do by falling back to familiar territory - he's experienced at running parties full of weird and powerful people who hate each other, at this point.
Like, this whole thing is pretty obviously theater to put us on the back foot. Even if he's right about the sale of the house being illegal, right now we're the legal owners until said sale is officially declared illegal, which is unlikely to be a quick process even with Hiashi willing to expedite it. Especially since said declaration immediately puts the Tower on the hook for the money we paid for the house. So Oro definitely came in with the purpose of gaining power over us and starting whatever negotiation he has in mind with an advantage - I'm not sure what it is that he wants, but I'd bet on it having to do with the basement; wouldn't be surprised if the private conversation quickly circles to what we found down there, exactly.
In any event, I think we need to stall, likely deploy heavy-duty social weaponry in the form of Mari and Ami against Oro, and get our bearings in the meantime.