1) What is my recourse to getting this lien waived/released on my property?
I went through something like this many years ago- it didn't get to the point of a lien being filed because I was tipped off in advance and called my attorney immediately. And yes, it was about drywall. I had paid the contractor in full.

He said that it would be a case of slander of title and we would immediately sue if a lien was filed. Understand that this was in Ohio and your experience may be very different in Illinois. Contact an attorney asap.