I guess I missed one important element to my suggestion:
This would only pass LEGAL (not necessarily Constitutional) muster if CFB would initiate some sort of unionized employment system, and only then if collectively bargained (e.g., the NFL, NBA, etc. players associations)
Otherwise, NOT the U.S. Constitution, but Antitrust law, State and Federal Employment law- especially regarding government reluctance (or outright prohibition in some states) to enforce non-compete clauses would be the issue.
I am usually not one for unions, but a CFB CBA might just be the answer in this situation. Maybe the future CFB Commissioner (Nick Saban) will agree....