I am teaching an elective course in which students' grades are determined on the basis of a final project. Due to unforeseen circumstances, this year I had to grant a one-week blanket exception to all of the students. However, several students asked for, and received, an additional extension beyond the general extension, based on legitimate issues related to other academic commitments.
Unfortunately, some of these students have still failed to turn in their project, and this is leaving me at a loss for how to proceed. For this year, I have decided on a policy of deducting a full letter grade for each 24 hours beyond the deadline, but this at once seems too harsh (to the individual students affected) and also too lenient (because everybody else managed to turn things in on time).
Is there a reasonable way to handle tardiness in submissions of final papers or projects, particularly when they are the sole basis for determining a grade?