Another option is to create a cohort, assign all the users once and then enroll the cohort to the classes. It's pretty easy. You can even assign people to the cohort by bulk upload...takes a little brain...I don't remember quite how it works but I tried it once and it was fine.
You can also use the Bulk user actions in Site administration (if the users can be searched/filtered there) to assign to a cohort. This is a little harder for me, as the criteria I'd filter by doesn't show up in this area.