So I have cooked two batches of hard boiled eggs since my original post. Same pan, same style: water with vinegar.
One, commercial/store-bought eggs, all with a uniform Coppertone tan, and again, loogies of what seemed like paint sloughed off into the cooking water.
A second batch today: farm eggs. All brown but various shades of beige, pink and brown. Nothing sloughed into the water. The darker eggs got splotchy and were less uniform in color after the cook, but other than some egg white that seeped through a crack one egg had that I wasn't aware of, there was nothing in the cooking water.