^^^^ This!...or you could just feed an 'all flock' type feed and provide oyster shells in a separate container.
I like to feed a 'flock raiser' 20% protein crumble to all ages and genders, as non-layers(chicks, males and molting birds) do not need the extra calcium that is in layer feed and chicks and molters can use the extra protein. Makes life much simpler to store and distribute one type of chow that everyone can eat.
The higher protein crumble also offsets the 8% protein scratch grains and other kitchen/garden scraps I like to offer.
Calcium should be available at all times for the layers, I use oyster shell mixed with rinsed, dried, crushed chicken egg shells in a separate container.
Animal protein (mealworms, a little cheese - beware the salt content, meat scraps) is provided during molting and if I see any feather eating.
Up until a couple of months ago, I feed my 1 1/2 yr old hens chick starter crumble. I liked the higher protein and feed oyster shell on the side. I recently changed brands and went to a 20% all flock. I have adults, pullets and babies on this. All love it and are doing great!
This was my brooder. It was a permanent structure inside the coop. I had my roost on the top, and used the top of the brooder as a poop board. It worked really good. It was 3'x10'.
Then I got tired of scraping poop every day, and tore it out and redid my coop. Instead of one large coop, I made it into 2 coops and then added another coop on the other side of that wall. Plus each coop has an attached run.
What you can do, instead of building it inside your run, you can build it on the outside with an opening to the run. Then it wouldn't take up run space, and you wouldn't have the chickens trying to roost on top. Or if you build it in the run and don't want the chickens on top, make sure you build a slanted roof.
Now, I just have the babies in the coop/run that is between my other two coops. They can see the adults and interact with them safely through the hardware cloth. When it's time for them to join the group, there is very little pecking since they have been side by side since I brought the babies home.