I would like to provide a free paid version for university students
You can get the same thing on core as the paid version. The paid version comes just pre-installed a lot of stuff, which can easely be downloaded in the software center.
As @Storm said the only difference with Pro and Core is the pre-installed software and I think 2 Desktop Layouts. Pro licensing is more to keep the project moving forward and funded. But ll benefits and features are there for core users.
Isn't there an education version designed specifically for this sort of thing?
I could be wrong* but I think when I checked Zorin Education out, it was more geared toward primary (k-12) over University applications.