They must be willing to eat their own dog food or else the question won't make any sense for the interview.

The department should run the interviews through their own employees first. If some questions cause an "interview anti-loop" (a set of other employees S who would not hire E) it's time to revise those questions.

Revise and rehearse these practice interviews within the department, and do it blind, until all of S are willing to "hire" each other for their respective roles.