This is a really serious matter, that should be adressed ASAP.
Either via Party Finder option aka "Only 2 chests people allowed" or, via some big announcement when someone join your party.
Also, nickname should be included in that. You don't want to sit there asking "who is cleared already?"

p.s. Thanks for pointing this out, because i was thinking, that it works exactly the same as Alexander, and.... it's not.