You have no leverage

No, they won't change layoff to fire, and they won't give you a better package.  The decision is already made, the HR person merely carrying out the execution. 

As an analogy, it's like in prison, you are trying to negotiate with a jail guard about changing your sentence while your sentence was made by a judge.  Here is the same, the HR person you talk to does not make decisions.  You either file a complain, or you take the package, there is no use to "wait" and talk to the HR person.

Take the package and move on.  Stop wasting everyone's time, yours, ours, and your school's.