The first summer's work resulted in a paper: "Enumerating Backgammon Positions: The Perfect Hash", Arthur Benjamin and Andrew M. Ross, Interface, Vol. 16, No. 1, pp. 3-10, Spring 1997.
"Interface" is (was?) "An interdisciplinary journal of undergraduate research at Harvey Mudd College". As you might expect, its archives are not easily available to the public. If you would like a copy of that paper, though, please e-mail me.
In the years since that article was written, I have learned that the problem we discussed is similar to describing the system state in a closed Jackson queueing network, or to the system state in an M/PH/c or PH/PH/c queueing system. There are published algorithms that work on these types of queueing systems, and it is quite possible that their state mapping is the same as the one we developed independently for backgammon. I just haven't had the time to investigate further. To learn more about my queueing research, go here.