Coasian Scheduling

We did scheduling for my job with GMU housing last week in a manner that at times resembled varying degrees of mob rule and slightly organized mob rule. It took two hours, was not fun, and left everyone complaining that there must be a better way to do scheduling. There are 15 shifts/day, 7 days/week. The only condition is that nobody can work two shifts at once (some are duplicate shifts) nor can they work more than 40 hours in a week, while my boss would prefer that everyone work about 30 hours.

My first thought was to establish a market and have everyone bid on shifts, but as many of my co workers have other jobs that pay more per hour (Housing has a low hourly pay rate, but comes with the fixed benefit of no cost summer housing), it is easy to imagine enough employees strategically bidding to minimize their hours in a way that would make completing the schedule impossible without forcing some employees to work overtime.

Since it is easy for us to trade our shifts with each other, it seems like Coasian bargaining is a possibility. If original allocation doesn't matter, each employee could be given all 15 shifts for a particular day, and then made responsible for getting them filled. Or if employees wanted a greater sense of control, an order could be made and employees could be given 10 seconds to make their pick, failure to pick within 10 seconds would result in being assigned the earliest vacant shift (i.e. Monday at 8am, then 10am, then noon, until all of Monday is full, then Tuesday at 8am...). With 11 employees, this would mean that everyone would be given almost 2 minutes/ pick and 105 shifts/week could be filled at a rate of about 1 month/hour.

As it is, all employees submitted their hours of availability to a single employee now in charge of scheduling "on a trial basis". Since we are still able to trade our shifts, I don't see any problems with this aside from the fact that the scheduler will certainly receive the most convenient schedule. Are there any other methods for scheduling that could be employed?