Cute flock you have, and great looking coop. Congrats.
I'm gonna be partial to Eleanor your BCM and I love the name simply because it was in the movie.. 'Gone in 60 seconds'.
For an immediate fix, set a tote lid on top of your wire. Most of the spilled feed can be dumped back in feeder. I do this out in the run also. The bigs clean up anything else.
My BCMs stick closer to the coop than the mixed flock does. But I've got crop fields on 2 sides so it's not an issue with wandering too much until the corn gets high enough the coons can move freely during daylight hours without being seen...another reason for fencing. I have Hawks and...
I have a couple big ones also having a Bull Mastiff but I will wrap any I need for young birds with hc and zip ties.
Pretty simple but it protects against pecking injuries and coon hands, or smaller predators getting to them.
And yes, the littles should start following the bigs in at roost...
How big are the openings? I've wrapped my wire crates with hardware cloth to prevent pecking injury.
How big is it? Can you add a roost for them?
Next question is how secure is your run? If it's not secure, I would transport them back and forth into an enclosed garage or similar if the coop is...
You could use these for the kennel to coop..
For your chicken door, you could frame it with wood, staple the wire to wood. Cut wire hole and attach pop door with hinges to wood frame.