SO...
I'm going to defer to Eggcessive and
Wyorp Rock (above) on all things related to poultry illness and injury.
As with most here, I generally recommend relying on a well formulated commercial feed to ensure your birds get the nutrition they need, and am happy to advise on what I look for in a commercial feed and why. Making your own well balanced feed is hard, and its not economical for most - I've often said that the more I learn about feeding chickens, the less inclined I am to attempt to mix my own.
Would need to know a bunch more about your feed regimen to start doing the calculations, but since only one bird is seemingly affected, my first thought is NOT your feed.
From description and photos, I'll offer two things, but no conclusive diagnosis. First, that sounds a lot like a hard molt. There is almost nothing you can do with chicken feed to make that go faster. There are a lot of things you can do with chicken feed to make that go slower. Wait, what???
Molting requires dropping and replacing feathers. Feathers are made mostly of protein, and specifically the protein beta-keratin. Beta Keratin is made mostly of glycine, proline, serine - all amino acids a chicken can manufacture on its own, and all AAs readily found in the diet. Also Cysteine, which a bird can get in part from diet, and in part by conversion of Methionine (they are both sulfur containing AAs) with the addition of serine.
Because a chicken can't effectively store protein (they excrete what they don't use each day), there are two practical limits on the ability of feed to affect speed of molt. One is the amount of protein your bird can convert into feathers each day, the other is the amount of Cysteine + Methionine in the diet. As a practical matter, Crude protein numbers above around 20% see rapidly diminishing returns, and Methionine levels around 0.4 to 0.45 will ensure more than adequate sulfur containing AAs to support a molt ASAP. But if your feed is 20%CP with 0.35% Met? the molt will complete almost as fast.
If its 16% CP with Met levels at 0.3 (or lower, in some Organic and soy-free feeds), you can reasonably expect molts to take longer. How much longer isn't well studied, and no doubt varies substantially by bird and environment.
That's the first thing.
The second is that whole illness injury I defer on. Your pics of the fecals (thanks for sharing, BTW - surprisingly useful when diagnosing chicken issues) have a lot of "white stuff" that looks like intestinal shedding to me. There are some dietary things that can do that, and the occasional normal shed, but intestinal shedding is often result of illness from things like coccidiosis or clostridum - keep an eye on that. Both are often present in the environment (coccidia are EVERYWHERE humans have been, even space), and only an issue when they exceed the chicken's ability to naturally keep in check. They tend to be opportunistic infections, when a chicken is facing other challenges as well - like weather and hard molt. Keep an eye on that. If it continues, I'd suggest treating for a suspect case of coccidiosis. Its cheap, there's basically no downside, and either it resolves the issue or you rule it out as a possibility.
That's all I've got. and I really don't know much more about feeding chickens than you could learn for yourself in a couple weekends of focused reading. Hope it helps.
The crop should empty overnight and the crop will feel deflated like a balloon or empty sac in the morning before the hen has had anything to eat/drink.
