That sounds like quite a set up. Do you have pics? I'm considering a coop just for broody use.We put broodies in boxes we originally built to brood chicks to keep them organized. Each box is about 3' x 6.5' with lid doors at both ends. The boxes go right on the ground in the coops.
We can put a double nesting box at one end and food/water at the other end ... the nesting boxes are double ... with a divider. We line the top with empty feed bags so the broodies don't get pooed on. We also wrap the nesting box end in feed bags for broody privacy/seclusion.
We start two hens at once in the same double nest box. If one hen gives up we can start another, or we can combine the clutches under one hen. By having two hens brooding together and hatching at the same time we have two hens co-parenting one shared clutch of chicks. I think that's good during integration. We haven't lost a chick yet.
We have three boxes like this. We can start them in one box and later pick up the nest box with the hens in it and move it to another box. The hens tolerate this move very well. We have other cages we could use in a pinch, but we prefer these long narrow cages for brooding.
As soon as the chicks are up and around and the broodies are cooperating, we chase all the other birds out into the run and close the coop door, then roll the broody box on its side and get the chicks/hens to explore he whole coop. The rest of the flock comes to the wire side of the coop to check out the babies through the wire. Then we put the box back in place, empty, and open the coop doors for integration.