It's a strange one really and an easy one for the FA to get out of. All they have to do is relegate them and ask the EFL not to accept them in their leagues because of the blatent cheating. That way the FA will be forced to keep them in their competition.
The the FA will pay the runners up in the Championship final a few million to keep quiet and fanny is your aunty.

Sorted! Nothing to see here! Move on quickly and quietly please!