part of an RIF and the "severance" you are requesting is severance pay. If that is the case, I would submit a request to HR with a cc to the top Operations person at your site. No need, at this point, to involve an attorney. That may come later.
If the manual says that severance pay may be granted that means it has been granted in the past.
I come out of manufacturing (also in Illinois)and standards for severance are different for every industry. That said, you are a professional and 2 weeks per year of service is not unreasonable.