Try something like this?
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The white wire in front is just a closet wire shelf that's kept in place with bungee cords. It's about 16" tall so I can easily step over it. It's not that chickens can't get out by jumping it, just that most won't bother. I've accidentally left the run door open for a few hours and the chickens have always stayed inside.
I don't think that would stop some of them.
I have a couple POL pullets who fly out past my head if I don't raise my hands. The other day I had to change my shirt because one bounced off my shoulder and left a poopy footprint.

Mature hens, yes. But those POL girls are wild and crazy.
I only want 4 - 6 chicks, but I might try to make the coop a little larger and enclose the nesting box in the main part, up against the wall, instead of adding it onto the side in a separate box.
Unless it's mounted high enough that the birds can easily walk around under it, the space the nests take up inside don't count -- which is why most small coops have them mounted on the outside. Also, there is the risk that hens would decide that the dark space in the back corner under the nest where you can't reach would make a perfect nest.

I've got nests inside Neuchickenstein (with outside access), but that coop is 16x16 -- plenty of room to spare -- and the nests are mounted at elbow height for me.
The easiest way to enlarge the Little Monitor Coop would be to lengthen it to 6 feet along the length of the monitor (which takes care of adding additional ventilation), move the access door to the side opposite the wall, and turn the roost to run that way instead of across.
You would want to make sure that the altered access door was wide enough to reach every corner of the coop.