Acknowledgements: Full credit to Tom Case on the MacAdmins Slack for this tip.
It's not immediately obvious that you can import custom .mobileconfig profiles into Mosyle MDM, but apparently you can if you go to Management > Certificates > (click on profile or add new one) > Select the file.
Those can be any .mobileconfig files—they do not have to be actual certificates.
If you're getting errors like Websites are turned off. An administrator can turn them on using the Server application or the configuration for your ipad could not be downloaded invalid profile, try Reset Apache In OS X Server To Factory Defaults and then turn Websites and Profile Manager back on.
Don't know how many Mac admins out there are actually using Server.app's Profile Manager for MDM, but I found a weird little quirk to it that's weirder than the other weird quirks about it.
If you disallow renaming the device by unchecking the box in iOS Restrictions, it doesn't just restrict users on the iPad from renaming the device—it also restricts Profile Manager itself from renaming the device!
So if you have some renaming you want to do on supervised devices using Profile Manager, you may want to uncheck that box. Very odd...