Is there a way to remove/suspend/block a SIS-added user from a course before the SIS is updated?

[mbmacdonald]

Our enrollments are created/updated by automatic SIS import every 2hours. I recently had a situation where an enrolled user needed to be immediately removed from a Canvas course (not be able to access anything). Obviously I can delete the user or deactivate the user's enrollment, but they will be re-added (with an active status) every 2 hours until the SIS is updated.

Any ideas?

I hope it goes without saying that "make the registrar's office work faster" is not a solution.