I feed the same feed year around except when I have young chicks in the flock, then they all get a high protein chick starter for a month or so. Otherwise it is a lower protein low calcium feed. I offer oyster shells on the side so the ones that need the extra calcium can get it. The ones that don't need that much calcium don't eat enough to hurt themselves. Mine forage for so much of their food I can't micromanage how much protein they get. They lay lots of eggs, hatch and raise a lot of chicks, and can fly down form the roosts without being in danger of hurting themselves on landing. In other words, normal chickens.
When they are molting they are not laying. The nutrients that were going into making eggs now go into making feathers. The speed of the molt is controlled by how fast the feathers fall out, not how fast they grow back. How fast they fall out is controlled by genetics, not what they eat. I personally do not see any benefit to increasing the protein content when they are molting, that does not affect my goals. I don't see anything wrong with feeding our dual purpose chickens a high protein feed when they are laying or molting, but I also do not see a benefit with my flock and goals. I want them to be able to safely fly up to my roosts and back down.
Chickens do molt from the head down. Checking her for mites or lice was a good move. Did you check at night for roost mites? Those only come out in the dark so you need to check for them with a light. Look in the vent area, they like the moisture there. And be fairly quick, they will run from the light.
Feather picking is certainly a possibility.
Is she broody? Sometimes a broody hen will pluck her breast feathers to expose more skin to help incubate the eggs. A photo of the feather loss could help.
Good luck with it.
