The damaged and blackened finger nail finally came off this afternoon. I will admit that it had a little help from me. Washing the dishes certainly helped to loosen it up, and when it was finally hanging by just one corner I gave a gentle tug and off it came.
The proto-nail underneath is about half or two-thirds the length of the nail bed, with a fairly deep crease running across it about mid-way. The crease is likely where the door made the most contact and broke the bone inside.
Having the black nail there was a constant reminder of what had happened, and while I didn’t think it was too unsightly, I was aware that it stood out a bit. Seeing my finger without the black nail is good, only time and patience now will determine how the nail re-grows.