You know, most of these problems can be avoided if you accept assignments late and have most of the course grade depend on one or more large individual projects that must be turned in "sometime before the end of the semester". The simplifying assumption is that a student who doesn't try to learn anything deserves to remain ignorant -- it's nice how neatly this works out.

I give my students a recommended due date, but allow them to turn in any assignment at any time before Finals Week without penalty, for any reason. It works better than you might think.

(I wish that I was allowed to insist that everybody do an individual project. There is so much cheating it's a bit ridiculous, and the worst part is that the students who cheat are just good enough at covering their tracks that I can't find absolutely definitive evidence. This is especially common among Chinese students, for some reason. Again, I figure that if people harm their own learning by cheating on assignments, then their actions are self-punishing.)