Well, I was able to pry the coil (via that fragment) away from the perimeter of the hole using a spade bit. I also bought a funky two-jointed plier that's long enough to reach into the plug well:
As I attempted to rotate this thing out, the end broke off, along with the mystery fragment:
However, I was still able to grip the broken end of the coil and try to pull it out. No way was this thing coming out, even with two hands. The end of course broke again at some point; I can't tell if it just flopped over or fell into the cylinder. But that's not the bad part: In the struggle with the coil, the pliers pressed the lens of my borescope against the side of the well enough to break it... and send a tiny shower of glass fragments and powder right into the cylinder.
Broken glass in an engine. What could be better?