In my chicken house I put an old dog kennel-type cage. I don't usually let chickens brood in the nesting boxes because the eggs and chicks are so vulnerable to the other chickens. Instead, I wait for a hen to brood in the dog kennel. When she starts sitting on eggs, I put a water container and a small bowl of food near her, and shut the door, locking her in. Sometimes, after a week or so, she will get frantic and want to go out. When this happens, I let her out and leave the door of the kennel open. Sometimes she comes back after a bit and I shut the door again. Sometimes another hen will go in and resume incubating the nest. And sometimes the nest is abandoned. It all comes down to chicken preference. I can't force her to sit. If she is frantic to get out, she is pacing and not sitting anyway, so she's not incubating the eggs. So it is pointless to try to force her. However, I have had great success with this method. When the chicks hatch, I remove them and the mom to a safer location (the chicks can get through the bars of the dog kennel, but the mom can't) where they chicks are protected from other chickens. When they are big enough to fly, I re-introduce both mom and chicks into the chicken house by putting them back into the dog kennel. Then after a day, open the door during the day and keeping it closed at night. Eventually, the mom will have the chicks perch with the other chickens and stop using the kennel. At this point, another hen has usually claimed the nesting space inside the kennel and we start the process again.
Maybe you could devise a similar system with your flock.