The coop is considerably smaller than yours, but the chicks sleep in there now inside a rabbit cage that I keep closed. I've also put up a cardboard box with a hole in it on the other end of the coop so they can find refuge on both ends when it comes to that. The run is large and technically can be expanded as needed. I have a permanent run as well as a movable fence that I move around so they always have fresh grass available. During the daytime I move the chicks out to another rabbit cage outside in the movable run (I only use the rabbit cage tops in both setups so they have contact with the ground/floor). I've set this cage up with food/water and shade, and have made a small door where they can get out but the adults can't get it. This is where I've let them together so far. The chicks will venture out but usually not very far from the cage and will be quick to run back in again if an adult pecks at them. We are only on day two of doing this.
I do have a small coop that I can place inside this movable run and have the chicks sleep there instead. Personally I was just hoping to get around this step, though I'd take that route if I don't feel fairly safe the chicks will be okay.