Not sure if this will be the same for everyone, but I managed to resolve mine by rolling back the firmware. Something Microsoft states in an article cannot be done.
Go into the Device Manager and under the firmware heading double click on Surface UEFI. Go to the driver tab and there will be a button to go back to a previous driver. If that button is greyed out, head to Google and search for Surface Pro firmware (I can't link at the moment). There is an official MS page that has all the past updates. Find the last update for the Surface UEFI and do ANOTHER Google search for that specific firmware.
I downloaded it and installed and it was already in place when I went to roll back, but you may have to roll it back on your machines.
I wish I had found this before I spent hours on the phone with Microsoft only to have them ignore me when I told them it was the firmware update that killed the Type Cover.
Hope this helps.