Great description Peter,
For reporting reasons, I would modify the /support/scp/newticket.inc.php to auto-populate the department and priorities once the Help Topic is chosen, and give them the ability to customize the department and priorities to their liking. This would make it so the "Help Topic" is always set and they can be populated from the database for statistical reporting.
If you find this to be a good idea, would you like help implementing something to this nature? (I've already modified /include/client/open.inc.php to do something similar for my use of osTicket)