I noticed this too with my EE's. I think in my case it's just not enough room in the coop. I know their awake at 4 am and I would go out to let them out but fear the preds.
When I first got chickens my SLW's, GLW's and Aussies got picked on so much I just gave them away. Some breeds just don't mix well and some birds are just not nice. Others pick up their habits. If you can separate the offending birds I would do that.
I even had a BR roo who killed a couple of his girls. All BR's a but for some reason he did not like these two birds. They did not want to go in to the coop at night and me not knowing kept tossing her in and one morning there she was dead on the floor.
Another girl would go hide outside somewhere but show up each morning. I feared for her and just posted her to CL and gave her away. She had nasty scrapes on her side.
I tried the "no pick" sprays and they just didn't work. You could try some Blue Kote.
Now my Dels they accept anyone. I have two smaller Frizzle girls and they're just fine. In fact I've had to keep an EE or BM hen from going in with them. They just wanted to be in with the Dels. Young chicks or birds and no problem.
Thanks Rancher, the Lav roo isn't bloody. The girls are just pulling his feathers out & eating them

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