Create a public Windows 10 P2P update cache?

I feel your pain. I also live and work in an area with poor Internet connectivity.

Your school district needs a WSUS server for its own internal use.  This then gives you some capability to schedule when updates to the server will occur. It also allows you to throttle server bandwidth usage by BITS based on a schedule.

You could then setup another server in a public subnet that uses WSUSOffline to pull updates from your WSUS server. You could then make the "Client" folder publicly accessible with instructions how to run the UpdateInstaller from that folder to install updates on whomever you trust with that info.

One drawback to this method is the requirement for 2 full stores of M$ updates. I would allocate at least 1TB for both machines just for updates.

A second drawback will be the amount of administrative time spent managing both servers. It "ain't" cheap maintaining a Microsoft environment.