@Adriaan van Dijk
What was the Moodle version back in 2016? Can see the specific build date in moodle code config.php file. That must have been a 3.1 or up to 3.3 if one had the latest/greatest syndrome.
Now when you say you have everything from that old decommissioned site, that means the code, the data directory and *most importantly* the DB?
If that's true, one could install VirtualBox on laptop with the same OS you were running that Moodle under. Restore the moodle site, then one would have the ability to export the quiz bank(s).
Do you have backups of courses from that old site? That's another way ... restore courses then work on exporting quiz bank(s).
Ya lost me ... completely ... do you have a similar situation? ... but if you have course backups then your situation different/easier, I might add. Just restore courses ... can exclude users and any other resource while restoring .. with the exception of any quiz - include those in the restore.
'spirit of sharing', Ken