I actually did find that article in my searching, thank you! I didn't find any examples that were quite like what my chicken (I assume it's the same one every day) has been laying.
I imagine nutrition could certainly be a cause, and as an added measure we just switched back to layer crumbles. We went through two bags of pellet feed, and we've been getting shells that are a bit thinner, even though we've been supplementing with oyster shell. Technically none of that should matter, though... it's the same brand feed with the same ingredients, plus the added oyster shell, which they didn't get before. A friend gave us a bag, so we're using it. I just don't understand the otherwise hard shell, with the one soft spot. It's as thin as paper over that one spot. Now today I didn't get an actual soft spot, but you could see where it would normally be.
I'm wondering if the birds are stressed, honestly. A few months back we added 4 new adults, and even though they are all getting along well, I wonder if they may mind sharing perch space at night. The coop is big enough for them, with enough nest boxes, but just big enough. They do free range all day in about a quarter acre of fenced yard, so they're not stuck in a small run.
I only wonder about them being stressed because of a few other oddball eggs we've gotten... eggs with colored patches from them touching in the egg shooter, and oddly shaped eggs, plus quite a few dropped from the roost at the end of the day. But then we've had some paper-shelled eggs, too! Not quite shell-less, but so thin shelled that they split open in the nest. We even had 3 fairy eggs in the past 2 months!
I'm just not sure what's going on, and haven't seen anything quite like these eggs online anywhere.