So how much protein total are you feeding? Has she molted before? What breed? How many birds to how much space, free range?
Greens, of what kind... they are mostly water and void of nutrients. I would forget the oats and the greens and just stick with the formulated ration and a little extra protein.
What does the skin actually look like? Even though you say no mites... did you know that depluming mites are microscopic and live inside the feather shaft and you will NEVER see them but only the evidence of them. They CANNOT be treated with standard surface treatments as they are systemic it requires something like Ivomec which is not approved for poultry so not much info on withdrawal time for eggs and such.
So you already saw her molt this year? Is she laying?
There is a product called pinless peepers to stop feather pecking. I haven't used them but if it is truly behavioral then it might help.
What do you feed including treats and supplements? (what is your actual protein%)
Ever done a fecal float to get a worm species and load count? It's possible for something like that to prevent the nutrients needed from being absorbed. But I wouldn't treat without first knowing I need to but second knowing I am treating the right species.
How long have you been "increasing" protein for? Things don't usually change over night and might take 2-4 weeks to see real improvement. However if the improvement in nutrients happen but a bad habit has developed then the peepers might be a good idea.
How long have you had these hens?
Good luck getting it figured out.
If it was an individual problem and not something created by me or that I could remedy... I would cull.