I was about the post this when I found yours.
I also have this same question. Would be very helpful, especially in a lower elementary school setting where a teacher would struggle for awhile having kids change the settings.
I don't see anything in JAMF that would allow setting the Control Center so I am guessing it is not there, but wish it were.
I am trying to figure out the same thing with the Control Center - We currently have 1300 ipads that are shared and Administration is demanding for kids to be able to screen Record from the control center. How do I create a Configuration Profile to allow Screen Recording? Thanks.
Can we even use the screen recording on shared ipads? I see it works for teacher ipads and not shared student but not on shared student ipads. The Control Center Setting is gone when you go into settings.