So, Mark, one of the managers at the insurance company, called me this morning around 10am.  He was very polite and listened to my description of the problem and all of the background information.

He quickly dismissed the insurance company's liability for any problems I'm having though.  I mentioned to him the blurb I found on the estimate regarding their "Promise".  He was surprised to hear about that as he's not familiar with having that sort of text on an estimate.  I told him I could fax it to him, which I just did.

It sounds like he's going to lean on the body shop to have them own up to having installed the quarter-panel incorrectly.  But he said if there was something that should've been replaced or done that wasn't included on the estimate, he would certainly own up to that and cover the repairs.

I'm guessing all of this will go nowhere.  The insurance company will say it was improper installation that caused my problems, for which they are not liable.  And the body shop will say they are not liable for rust problems, even though the rust is a direct result of poor installation.  But it can't hurt to try to get someone else to pay for the work, so we'll see where this leads.