Since this is at least the 2nd time this has happened during a swap that I know of , maybe it needs more structure regarding participants. It might be a good idea if anyone participating be asked to pay a one time security deposit to be held in a “club” account, until they withdraw from the swap “club” - that should ensure only honest participants and offer security if someone does slip through or a doll is damaged. It would require one or more persons to be responsible for setting up such an account, but it should deter any theft activity if they have to invest something and go on record for that investment.
Further, proof of identity might be a good idea too. If someone wants to participate, then they should be able to provide that and the “club” should keep a copy of names & shipping addresses.
These are just some thoughts that probably needs some fine tuning, but it might be food for thought.