Relationship between KS, AUROC, and Gini
The Wikipedia entry for Receiver operating characteristic references this paper for the Gini=2AUROC-1 result: Hand, David J.; and Till, Robert J. (2001); A simple generalization of the area under the ROC curve for multiple class classification problems, Machine Learning, 45, 171–186.  But I'm afraid I don't have easy access to it to see how close it comes to what you want.