And enforce no minimum bids, therefore they could pay zero for loot only they want, and you'd even prevent the 'forgoing early upgrades' problem.

So they would pay the second highest bid in addition to their own? Or..what? Sorry, I'm new at all this, and that confused me a bit

I know it sounds crazy, but in a closed bid system (where people don't bid and then listen to other bids then rebid like in classic Auction Houses), having the winner pay the 2nd highest bid price is the fairest way to bid. It's actually the same system EBay uses, albeit in a slightly different manner - let's say person A bids $50 and person B bids $100. Person B would be listed as the winner, paying $51. The extra dollar is a triviality to make things seem more fair to the uninitiated, the effect is the same.

http://www.beyonddiscovery.org/content/view.page.asp?I=3685

There are other "fair" closed-bid systems, too, but this one is very effective and simple to implement. Basically, it encourages people to 'game' the system in a fair way by simply bidding their entire DKP pool every time they want an item.