We've noticed the same thing! At first, I tried to break her broodiness...no luck. I could have tried one method a little harder. I put her in the grow out pen with the younger group. If she would have stayed broody in there, it would have been fine but she didn't. Then she was sleeping on top of their little coop, and I felt bad about it and put her back into the regular coop at night, and didn't follow through with removing her the following days.
Then, she went full broody in the main nesting area, which is one large box that 2 hens usually lay in at once. I've even seen the bantam cochin squeeze in the middle once. So we set up separate nesting boxes on top of the main one and convinced her to stay. Now she gets out and lets the other girls lay in it...
We marked the 2 eggs we're letting her sit on, with plans of finishing them off in the incubator and hopefully breaking her broodiness once the incubator opens up and I feel like putting more effort into it.
That being said, their egg production has dropped by almost 1/2. Of course the EE isn't laying anymore, since she's broody. One of our red sex links who hasn't taken a day off in months, has taken 3 days off in the last week. Our Cream Legbar that had been laying 3-4 a week gave us 1. The other sex link has taken a couple of extra days off that she normally doesn't. The turkens seem to be the only ones still laying on their normal schedule and offering to lay in her nesting box. The bantam cochin hasn't been a strong layer for us so not much change. We believe one of our other CL's started laying a week ago but other than the 1 egg, we haven't seen anything from her so its possible the EE laid 2 before she went broody, that was the last day she laid, or the CL did lay and we just need her to get into the program full swing.
If I had it to do all over again, I wouldn't have let her go full broody. We were getting almost full counts on eggs for a few weeks up until about a week ago.