How to have a multi-criteria lookup find the most specific result when multiple results are possible?

Example File

I've never used google docs before to share, so let me know if that link doesn't work.

I created a test doc similar to the real doc I'm working on. Essentially I have data that utilizes multiple columns of information to create a unique scenario. I need it to look up the result from a seperate sheet based on the most specific data it can and give me the result.

For example on my test sheet:

State - Ohio, City - Cincinnati, County - Hamilton, Township - Delhi, School - Oak Hills should pull results H from tab A and 8 from tab B

The issue I run into is that from tab A, the results H, I and J could all fit for the data point in the example above. So figuring out a way to only produce the most specific result (specific being the furthest column to the right) as well as account for any data points that include "All" instead of something specific.

Any creative solutions for this?