My question involves labor and employment law for the state of: Illinois

I was terminated without cause, in a Reduction in Force initiative several weeks ago from an Executive position for a large global organization after only 6 months of employment. The termination came as a surprise as I was recruited into the organization by a senior executive and the position was created as a result of my recruitment. I am female over 40 years of age. During the termination meeting, HR neglected to provide a Schedule A or advise me of my rights to confer with a lawyer. I have not signed documents to date. Shortly after my termination in speaking to another terminated employee that was not eligible under ADES, he informed me he received the Schedule A and provided me with his copy. Upon review of these documents and my separation letter, I sent an email to HR requesting a) a copy of the Schedule A, and b) a revised severance that provided 45 days as opposed to 21 based on the group RIF status. Additionally I asked for all my employment records be sent to me and that all Electronically stored information (ESI) related to my employment be saved. Additionally, I requested that the 2 week severance and 10 day cancelation of health benefits, be extended to 12 weeks severance and 10 weeks health benefits. A reasonable request based on my officer level status and the circumstances surrounding my hiring.
HR replied with a revised severance letter to reflect 45 days, but changed my 'last day worked' to 10 days after my termination date. They also revised the 'Schedule A' to only include myself and one other terminated employee, where the original had 46 people in the decisional unit for termination, which 70% were over 40. Additionally they rejected my separation benefits counter offer. I replied and questioned why the Schedule A was revised, and they immediately referred me to their legal counsel.
As questionable and sloppy as the termination was ( and continues to be) my only objective is to receive an extended severance and health benefit agreement. The employment was 'at will' so I don't have contractual leverage. What is the probability that I can leverage the mismanaged termination, the revised Schedule A and termination date and circumstances surrounding my recruitment, for a better severance package?