Hi N,
Another thought -- do you think it would be valuable to also have the enrollment date and enrollment time tied to calendar entries? That way, when a student logs in, his/her calendar can already be marked with the day their class opened and the day their class "closes"
Then the info can be represented as an upcoming event!
This would somewhat produce a reminder to students, though it would probably not be as effective and "unarguable" as the countdown block or notification 
I love moodle!