How to prove receipt/no receipt of work?
I doubt this will work with 200 students, but the first thing I do when I collect assignments is check to see whose assignment is missing, and send the relevant students a message via the class messaging system. This does two things:


if there was a slipup at either end, this catches it quickly. Most often, the student says that they're turning it in late (I have an automatic submit-late-and-get-deductions policy). 
By using the class messaging system, I'm on record as having asked the student about the missing assignment. If they complain a week later that they did turn it in, I can point to the message and ask why they didn't respond to it.