@amurray , as a teacher, I've long been concerned by this very problem--and as a higher ed teacher, I hasten to add that it's by no means confined to K-12 courses. Indeed, the problem is somewhat exacerbated in higher ed. The common wisdom here seems to be, "Students prefer the consistency of having all of their assignments [in a course] due on the same day." However, from my (admittedly subjective) perspective, every teacher seems to want to have assignments due on Sunday at 11:59 pm--and because such a large proportion of our teachers in higher ed are adjuncts, they are all acting independently and are independently arriving at the same personal workflow accommodation.
I've used professional development sessions, which is one of the few occasions on which I'm able to interact with other adjuncts, to conduct my independent polls on what day in the week works best for others as a due date, simply so I can avoid that day in my own courses. 
One solution I devised for my own courses is to stagger the course work for students. That's not to say that assignments are due on a different day each week; rather, I split the workload into smaller assignments so that they can be spread out across the week. Over the last few years my courses incorporated a low-stakes graded quiz that was due on Tuesday (which meant the student needed to have at least skimmed the assigned reading by Tuesday), an in-depth quiz on the chapter due on Friday (requiring the student to have mastered the required reading and at least skimmed the ancillary materials), and a short writing assignment due on Sunday (when students ultimately demonstrate mastery of the subject matter). Each assignment contributed a successively larger amount to the course grade: 0.5%, 1.5%, and 3% respectively. Most students seemed to appreciate having their work spread out for them in this manner.
I'm hopeful your insightful question can inspire others to share their solutions in a comprehensive discussion of a problem that undoubtedly burdens many students.
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