Adding another “test” or bit of data to weed out the uber geeks.
This cannot be done alongside the ecclesiastical endorsement. It’s basically a job interview so there should be some element of risk. Your uncle can’t interview you for example.
There is a long list of schools, and not just ivies that either require or recommend an interview.
Could begin by recommending one and see how that flies. Doesn’t even have to be a hard data point it can be done as “informational”.
It’ll quickly become a de facto requirement as everyone will assume they’ll stand out if they don’t do it.