I am new to this but I have heard in the situation where you are introducing them to a flock to avoid that its good to give them distractions like toys or objects that take their attention off each other. One example I read stated that they put a Cd hanging in the run and i guess their curiousity about it was diversion enough. I am sure there are other ways to prevent it as well. Good Luck!
How much scratch? If you're mixing them, there's your problem. Most commercial feeds have barely over minimum protein required for healthy layers. When you add the scratch, you dilute the protein. Chickens will cannibalize each other (feathers are high in protein) in order to try and recoup that. At the same time, chickens are like children and scratch is like candy. They will pick through the food and eat the candy first.
Scratch is a treat and should be no more than 5% of their total diet. For now, get rid of the scratch and feed only the layer feed. If you want to quicken their recovery, offer a high protein (preferably animal) treat or switch their feed over to game bird and offer some oyster shell on the side for calcium.
Providing more detailed answers to the questions asked above will help us to answer you -
for example, rather than 'a large space', provide actual dimensions of the space they are in - we are asking because often issues such as picking are related to underlying issues of overcrowding, etc. Your idea of "a large space" and the amount of space needed can often be different.
Regarding feed - what is the brand/specific formula you are feeding? Picking can be related to nutritional deficiency, so knowing what "layer feed" you are using is key to helping you try to resolve the issue.