I think that any carrier doing this now will charge what they can and it's 'take it or leave it'. Once they have quoted, they won't negotiate as that would lead more people to think they can lower the price that way. That was the problem with the era of 'free upgrades'.
I favour the quoted price over the auction process. What makes the auction clever (for the carrier) is that only the winner know what prices was actually paid, as opposed to any pax being able to ask.