Maybe there could be a rotation of the sacrificial fixer. Every month, one dev is given perks (private office, free food, a really big chair, ...) while they handle the back-log. They work under the guidance of the last fixer, to make the transition smooth.
When I toured Valve last summer, there were quite a lot of large empty offices. Everyone's desks were on wheels, and the workstations were set up to make them extremely easy to move. Naturally, with no management structure, anyone was free to take up an office, but hardly anyone wanted to.
The receptionist who was giving the tour, indicated that Valve had constructed more offices than people actually wanted to use, so they were considering tearing many of them down. Most employees preferred working in more open areas in the midst of the rest of their "cabal".
As far as other perks go, Valve employees already have a nice selection of free snacks, drinks, in-office massage sessions, etc... I'm sure there are ways to incentivize Valve employees to do less appealing work, and I wouldn't be surprised at all to hear that they already do this on an ad hoc basis, but they would have to go a little bit beyond your traditional office perks.
i'll bet something as simple as putting up a list of important if not very glamorous tasks somewhere prominently and continuously visible (e.g. large whiteboard on one wall), and then inviting people to choose a task and cross it off the list, would be motivating enough. note that the kind of self-motivated employee valve hires for usually wants to both make better things and make things better.
