CAS is an arbitral body, it's not a sovereign court. Any arbitration is only possible if the parties involve have signed a valid arbitration agreement. In this case, the EFL rules are the arbitration agreement and the arbitral panel was the band of eeejits cobbled together by the appointed resolution body. If the arbitration agreement says no recourse to CAS then it's binding.
However, an arbitration agreement must still comply with the law and cannot be used to create perverse legal consequences. So a court challenge is still possible.
I don't think we will do; but that's the framework.