Are you aware of the work on this topic, but relating especially to Catholic schools, being conducted by the Catholic University of Louvain? They offer the "Enhancing Catholic School Identity Project" (ECSIP) which has a twofold track: partly serious empirical evidence gathering; partly theological vision.
If you are interested in knowing more about this approach, put "ECSIP" into your search engine ... there's material not just from ECSIP itself but from serious educational journals. 

This is a Project that gives me optimism, precisely because it tangles with the "HOW".