I successfully moved the broody hen & eggs (just a couple of feet from where she wanted to nest on the floor of the secure run) into a 2x4x3 crate type cage that is nestled into a corner of the secure run. I lined the bottom with cardboard & 10" up the sides with shade screen to keep baby birdies we're expecting from venturing out. It has a door that can be left open until the babies are big enough to hop in & out on their own, or kept closed if the other girls get too pecky. Mama & chicks can stay in the broody pen for a couple of weeks after the hatch, then they will have the secure run (6'x12') to themselves in the afternoons while the big girls use the day-run (10'x100'). That way I can feed separately so I'm not dumping chick starter down my laying hens gullets

Just have to compose an alternate entrance to the hen house for my layers, or toss a nest box in the day run... except one of the girls is very particular and will squawk & screech at the garden gate until someone lets her out & she hightails it straight to the hen house to lay in her favorite spot LOL.
It sounds like you've thought this out well. If the broody hen gets upset about being within sight of the other birds, you can always place a sight barrier around the crate. I do have a few concerns about the details that you may have already taken care of, but didn't mention in your post.
First, is the crate in an area where other birds can jump on top of it? Chickens like to jump up on things, and the hen might get very stressed out about that. If needed, you can just secure a cardboard box to the top, modified to have a very slanted top, like an A-frame shape, but high enough that they can't roost on the peak.
Second, is the weave of the shade screen of a size that the chicks could get their toes caught in it? I am always amazed at what chicks get toes and toenails caught on. I put a tee-shirt in a brooder once and a chick got its toenail caught on a seam thread -- almost lost the whole toe to infection!! Luckily, the antibiotics worked well, but the nail is still a little twisted and has to be trimmed every month. Even if the screen is only on the sides, if it goes all the way to the bottom a chick will find a way to injure itself. You could probably just attach a 2" high layer of cardboard around the bottom edge to prevent any problems. Make sure that the chicks can't get between the cardboard and the screening and get stuck.
Third is the cardboard on the floor of the crate. I assume that was just to cover the bottom grate, and that you'd be putting some kind of absorbent bedding down, but just wanted to be sure. Cardboard might be too slippery for young chicks. They are so susceptible to splay leg when first hatched, and it is vital to keep them on a surface with good traction. There's lots of options, just as long as it's not slippery, toxic, itchy, cold, bad smelling, and they don't eat it.
Enjoy your chicks and broody.