Someone from the hospital filed a grievance to the insurance company on my behalf, and everything was corrected without me having to do anything. All of the claims went through and have been paid, and it turns out that I owe only one ER visit co-pay (I thought that I would have to pay two, for two hospitals, plus in-patient co-pays).
Tom and I were wondering why the hospital would do this for me, and my best guess is that they will get their money more quickly this way. It all comes back to money, right? Anyway, two thumbs up for Carilion.