The types you should be looking at are /education/institution and /education/university. Between them, they should have all the properties for post-secondary schools. (Educational Institution has properties that are common to schools of all levels.)
If there is data in your dataset that you want to load,and which doesn't match any existing properties, we can talk about adding new properties. The first place to start, though, would be to create a type in your private domain to hold those properties so you can test them out and so that people can review them before adding them to the types in the education domain.
This looks like a great dataset. Feel free to keep posting questions while you work on it.