You sir are a champion for putting up with this mess. However something is troubling me (outside of everything that happened to you). In the post you said "but I couldn't finish it in time so I e-mailed it to myself to finish at home,"
Is it possible for you to find the computer from which you emailed the assignment from? I don't know if that will help your case to prove that you didn't plagiarize anything but it could be a start. If that doesn't work then does the class room you were in have cameras?
"On the 16th, my class was assigned to read a paper and write 3 or so paragraphs explaining the author's purpose. I was not there for the assignment, so I received it when I came back to class on the 21st. I worked on the assignment all class long," If you can get the footage of you coming to class on the 21st, then you might be able to prove that you finished the paper on the 21st even though you turned it in two days later. (I don't know if anyone witnessed you working on the assignment but if anyone did then that might help your case as well).
"One of the main things that drove him to accuse me is the date difference. The top of the paper reads "21 February 2017" when I turned it in on the 23rd. If I were him, I would get the hint that I was there and worked on the paper ON the 21st."
Couple the above statement with the one about you emailing the assignment to yourself on the same day and you just might be able to prove that you did the work yourself...... I don't really know how to help beyond this but hopefully you can prove your innocence.