This is precisely the scenario most large districts find themselves in that result in hosting the server locally. Much of the work done during the day is by by teachers uploading and configuring the site when speed is critical to getting the work done in short periods of time (ie. between classes and during prep, lunch etc.). In my experience, the servers then get hit hard after 6:00 pm when the Internet bandwidth is low at the school. I tend to suggest that back-ups happen after midnight when use dies significantly.
Hardware and performance
Server Host options for School District?
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