Manually removing an orphaned entity type
In case it is of use to anyone else dealing with an old module that doesn't uninstall correctly. The solution to my problem was the following.
WARNING: Do this on a copy of your actual site and database. You could break a live site doing this.
Most of the troublesome database entries are in the config table.
You can use the error list produced above when trying to install the module to track down the rows to purge.
In the database a query such as:
SELECT name FROM config WHERE name LIKE '%support_ticket%';
should show you most of the problematic entries.
In my case that exactly matched the offending active configuration so i could just change the above to:
DELETE FROM config WHERE name LIKE '%support_ticket%';
I would be very careful about doing this with a LIKE query unless you are sure you won't accidentally delete something else.
I assume directly removing entries like this in the database is probably a bad idea but I really couldn't find another way to move forward.
Once the above is done Drush updb worked and the update completed.