Beautiful set up! Love the light in your coop - but that might be the reason they are laying in the dark corner.
I like my chicks and hens to work out integration on their own hook. I put my chicks in a dog crate at night, put the crate in the coop at night. Then the first few days, I put my chicks in a safety zone in the run. It is fenced so that chicks can get into it easily, but hens cannot follow them. Away from the safety zone - I set up a pallet, up on low bricks, another place where chicks can escape to, but hens can't follow them.
Then I let the hens out, lock the chicks in the run. I sit down there with my cup of coffee and wait until a chick gets brave enough to come out of the safety zone, and I give a mock chase back to the safety zone. They figure it out pretty quick. I let the hens in late in the day. Watching carefully for a bit. I want the chicks to venture out, escape back to safety, learning to respect the hens, but not letting the hens kill them. The hens get used to them pretty quick.
Then I just leave the dog crate in the safety zone, and after one or two times, they just go into it near dark, I carry it in to the coop. Once I see the chicks out and about among the hens I no longer lock them in the crate. I just leave the crate open, and generally by the time I get down to them, they are out and about. After a day or two, they find their way back into the coop into the crate by themselves.
I have a lot of hideouts - which I really don't see in your run. If you look, you will see that a hen can really see every other bird 100% of the time. You would do better to add more clutter to the run. This lets birds get out of sight and out of mind of the other birds, and makes more use of the vertical space in the run.
I posted a post on cluttered runs, and people posted all kinds of runs that had clutter if you want some ideas. Also, clutter allows you to put out feed in one spot, so that a bird eating at another sight cannot see that bird eating. Helps a lot.
Mrs K