Very nice Rick! I think you are right that this may be as close as you could get. You mentioned that the output does show some goodness of fit tests, you could use those to aid in your quest. Instead of focusing on the tests themselves one could ask whether THIS particular solution minimizes any of the goodness of fit statistics within the whole number bounds of the problem. That is to say that solution that would be better than the one you have presented would have a normal fit AND a smaller goodness of fit statistic.