I'm guessing that these are BYOD iPads the students are bringing? If that's the case and the Apple IDs are personal and not managed by the school, then I believe you have little options left. There are ways to get the devices into Jamf and be able to send restrictions to the iPads. You can even set timers for when the restrictions will be 'on or off'. Enroll them as BYOD devices or use Configurator to get the Jamf profiles on them.
My hang up is the 'Family Account Apple IDs'. I'm not sure how those work and if Jamf can take over control of the devices via restrictions profiles applied to them. This is probably a Jamf System Engineer question.
Whatever you find out, please share here! Good luck.
By the way, this is a very interesting question, and I think many people are interested in circumventing this restriction. But if a solution is found, can't it be used for bad purposes?
But, it is interesting to know if you find a solution!