My broodies like to brood in the laying boxes, usually two in the favorite laying boxes (I have two now). I let them do their thing, the other hens keep their distance. The laying boxes are about 2 feet off the ground so I put a board up to keep them from falling down but you'd be surprised how they learn to manage the ramp and mom has them out.
I freaked out the first time they did this but have learned they take care of them.
Oh, and I've never had luck moving them, so I let them be. After they all hatch I moved the first ones but then hen moves them back into the coop so now I just leave them.
similar experience here -- i just went through five broodies this spring, and i ended up with trouble with/from girls that got moved, smooth sailing with the ones i left alone. go figure.