You could install print tracking software.
We do some production printing. The users that can print to the production printer have print tracking software installed. Basically everything that's printed to it causes a pop-up dialog box, users select the project its being billed to and type in any details they want to add, like reprint error- do not bill, and click print.
The software we use, they have to log the job, or it won't print. You get accurate billing, pages, printed, file name, user, project, details, time and date, etc. And, its not something that would cause an employee to walk out over because of big brother breathing down their neck full time.