After some thought, we need to hack the quiz with an open-university-specific hack. We can control this using a $CFG->openuniversityhacks = true in config.php

The idea is to disallow "tutors" from seeing all the grades (reports) in a quiz until the quiz has finished.

So, we basically need to add a bit of logic like this:

$canviewhidden = has_capability('moodle/grade:viewhidden', get_context_instance(CONTEXT_COURSE, $this->course->id));

if (isset($CFG->openuniversityhacks) && !$canviewhidden && $quiz->timeclose && $quiz->timeclose > time() ) {
// FORCE THE QUIZ TO APPEAR AS FOR A STUDENT (NO EDIT, NO GRADE VIEW, NO REPORTS etc)
}