I leave brodys/eggs/chicks together in the main coop that has 10-15 birds at one time. I do not become involved beyond special water and food close to the new hatches. I did have one hen that pecked her hatchlings, and had to be moved, but normally I do about nothing. My current batch have been outside all day at 3 weeks, with there moms. It seems that special coops/heat/broody boxes make no sence when chickens are perfectly able to raise chickens in the flock enviorment.
I use a similar design although hen is allowed to roam with chicks for at least a couple hours each day. She can be allowed to return whe going to roost or enticed back in with chick feed. In a 4' x 8' unit like yours a game hen can rear 14 chicks easy.