Does the Airport Extreme log MAC addresses of devices that attempt to connect?
I was able to pull up the logs on the router, but unfortunately they were only for current day. I would have needed to export the logs to have a chance to catch the guy. Oh well, it was worth a shot.

To do this, I needed to install the airport utility v5.6 (in addition to the v6.x that was already installed).  The newer versions don't have an advanced tab which contains the ability to view "logs and statistics."