When I signed up for the Student Dev Pack originally in HS, the school district's evil IT department blocked mail from outside domains for whatever reason, so I sent GitHub a picture of my schedule (which had the name of the school and my name on it), and they accepted it. If you have evidence of being a home schooler (I believe there's some paperwork you have to file with the government?), they'll probably take it too.

And for the classroom system, it's open-source (https://classroom.github.com/) and you can run it on a box at home. That'd work given you probably only have a couple users at any one time.