Hi! I’m new to chickens and mine has just laid exactly what you have shown in your photo. I want to know what ever came of your case as it might help me. I had the same thinking, small for a lash egg, also it was laid with a shell less egg.
Mine was a pullet - had only come into lay recently at the time. There were soft shell and shell-less eggs. I didn't think too much of it at the time as others were still coming into lay.
After about a week of bad eggs, she started laying lash material. It never got hard, was more cottage cheese consistency, but quite a lot at times.
She was mopey and had a fever. I booked her in to the exotic vet, but they were full up and I had a several day wait. It was early days for me, so I treated her with garlic-covered dry crickets, a warm Epsom salt soak and ACV in her water daily. I did not remove her from the flock as the weather was pleasant and salpingitis isn't contagious - and she wasn't so sick she couldn't get around and eat.
She managed to clear the infection on her own and her fever had broken by the time she made it to the vet. She walked away with liquid calcium and some anti-inflamatories; never went on any antibiotics.
I'd had the girls on a premium grain feed before, but moved to pelleted after at the vet's recommendation. She had been laying double yolkers regularly before the soft shells started - my assumption is they caused an internal tear that led to the infection.
She no longer laid double yolkers after recovery. Her eggs were prone to minor shell quality issues and she was always more sensitive to heat after, but was still an egg a day once she recovered.