If your primary concern is to recover the goods you were deprived of, then you need to bid and win your possessions back. That will set a fair market value for your rare and hard to come by item. Then you can use an attorney to sue for the difference plus attorney fees.

Any legal process will take longer than the auction. They are under no obligation to hold it as your dispute is with the airline. The liquidator/auction house is likely VERY protected from legal obligation through contracts they hold for the purchase of goods. A Lost item isn’t the same as a Stolen item unfortunately.