As for feed, I was alternating between layer feed and all flock because I also have a rooster. Or sometimes mixing them 50/50. Oyster shell on the side. This pullet started laying 6 -7 months ago (same time, approximately, as the others). Since this started happening I've switched to only layer feed out of fear that she might not have been getting enough calcium in the feed (I don't know how avid an oyster-shell eater she is).Are you feeding a balanced diet of crumbles or pellets? Many people find that using peck and feed type rations allow chickens to pick out their favorite parts and may be deficient in some nutrients. Also having crushed oyster shell available can help with calcium. Shell gland problems can cause shell-less or thin shell eggs even though the chicken is getting calcium and vitamin D3.
Because it's very difficult to access the one vet who will treat chickens, I want to try what I can do in the meantime and really hope it solves the problem. But my first assumption was that it was something that I - and I'm guessing even a vet - can't fix (like a gland issue, for example).
Nice news, though: this afternoon she laid an egg with a much more substantive shell than I've seen in a while. I can't find any cracks and it holds up perfectly when I tap hard with my fingernail. Whether this will continue remains to be seen. Its shape is still different though, yet less abnormal-looking than in a while.
(I should post pics. I didn't initially because I feel like I've kind of hijacked this thread. But maybe I should since it's already gone this far.)