Howard Miller

What is "mod/studentquiz"? I assume it's this optional plugin https://moodle.org/plugins/mod_studentquiz. I've never heard of it before but it's certainly a candidate as the source of your problem.

It's probably worth asking the developers of that plugin for their thoughts. Or just removing it (if you don't use it). Also, check that you have the correct version installed.

You'd be surprised....

You should read Notifications. Especially the bit on admin settings.

Something is doing something.

I would probably start by checking the Network tab in the browser developer tools to see where it has got "stuck".

As an aside, I've been losing what's left of my hair working on a substantial plugin for Moodle to handle advanced grading and aggregation specific to our instituion (automating our administrative tasks that currently are done outside of Moodle). But the final destination of the grades is our student record system.

Also, just thinking about it, we make a point of leaving students enrolled in old courses so they can refer back to them. We created a role called "revision student" that restricts their ability to take part in activities when they may be mixed with newer students. That's rare because courses are generally recreated for each year/cohort.