I'd ask the auctioneer to value everything, or at least everything over a value that matters. What's a value that matters? Up to you - $100, $500, $1,000? The auctioneer doesn't need to talk to anyone to do this, and certainly the last thing any auctioneer is going to want is to be in the middle of a famlily meeting.
Then allow everyone to say what they want, send the rest to auction, divide the auction proceeds making allowance for what everyone has taken for themselves.
If more than one person wants the same piece, they draw lots. If there is more than one piece wanted by more than one person, draw lots for the order in which each person gets to choose, taking turns until everything is taken.