The CLA has a helpline and a walk-in help desk, so you should definitely call them up to ask about this. But I suspect that it will not be easy to get the $10K from your employer.
However, all is not lost. Since they are pulling this on you, and showing they are in the wrong because they’re paying you some penalty, you can negotiate with them to get something worthwhile. Perhaps a good recommendation from them, written on official letterhead. Get them to agree that they will not file your termination until you have found another job, so you won’t be deported because of their error in hiring too many teachers. And maybe they can introduce you to some other employers.