You're welcome. There are other algorithms fully covered in computer graphics textbooks (like Graphics Gems) that could be used to identify convex versus concave polygons. Another approach would be to treat it as a physics problem and calculate the center of mass, and then determine how much mass exists in the polygon far from the center. The mean and standard deviation for all county data could then be calculated.
Canada has an independent, non-political commission that makes determinations about gerrymandering, and I remember reading somewhere that they have developed algorithms to do this. If you intend to pursue, it might be useful to track them down and see what techniques they've made publicly available.