I'm imagining a large scale Vickery auction, sorry if I'm not explaining super well. Everyone pays the same, but people get a price they think is fair.
A Vickery auction would not, I think, lend itself to that kind of price discovery.
People could even bid "conditionally" for multiple sections, and once bidding closes you resolve the separate auctions in order from best to worst. If a person with multiple bids gets a good seat, their bids in the other sections get cancelled.
Seems to me that this could have very similar results as the dutch auction method, but each ticket is more fairly priced. Your ticket costs the same as the next guy, assuming they have a seat in the same section as you.
Edit: also, as mentioned somewhere else here, you're likely to have a threshold where everyone wants to buy once they see available seats start to disappear, causing a kind of "bank runoff" where everyone rushes to buy tickets all at once, putting us back where we started.
A threshold effect could certainly exist, that would be one issue with that scheme.
In that sense you could chose the system that fits you the most. I personally think that selling tickets via auction is indesirable for other reasons.