Suggest setting the Recyclebin to show all the time in the course admin menu as opposed to the default which is to display only when there is something in recyclebin.
Gives teacher/admin option to delete - which moves whatever to trashdir right away.
There is also a setting for how long to keep something tagged as recyclebin ... set that to lowest (shortest) time.
Cron jobs running ok? Especially at tail end where it picks up ad-hoc task - which are jobs that didn't complete the last run.
And .... there is a hidden tool for checking health ... site/admin/tool/health/ - run via browser - and might want to do that at non-prime time as the health check will look at quiz bank and I have seen a healthcheck spike memory usage for a long time.
When it finishes running it will show issues found and (hopefully) have some suggestions as to how to fix ... the suggestions will probably have SQL queries for you to run via command line or some other tool. Before doing those suggestion, make sure you have a DB dump!.