In a few minutes, I will be installing an extension to the Quiz engine, which should allow me to mass-close unsubmitted quiz attempts. This should allow me to correct the issue where an unsubmitted quiz does not show up in the gradebook, even after the due date.
Though I have tested this addition on another Moodle installation, there is the possibility of some instability, which should not persist for more than an hour or so.
The upgrade is complete, and everything has gone as expected. Thanks for your patience.