We keep our coturnix in one of the black wire dog crates. I attached hardware cloth around the walls to keep the bedding in , I imagine it would be possible to cover the cage with it to accommodate button quail as well.
I can't seem to upload pictures of that right now.
I keep all my quail indoors, we have a sun room that's mostly used for storage and I keep my cage-able birds and brooders in there. My quail brooder is an aquarium in the living room. It's way less worrisome for me with them inside because as long as I keep the kitties out nothing will eat them if they happen to escape I just wait till the calm down then walk over and pick them up, Of course they are my pets and I only have 5 coturnix quail, and my large dog crate works for them. As there are only 5 they don't stink unless the bedding gets wet , which is not often I have a rabbit bottle that they drink out. I put in a shelf and a ramp and decorated it with juniper branches to make it easier for them to walk up. And they have a dog bowl for a dust bath. I love my button quail they are totally adorable and fun to watch but coturnix are more calm . I can reach in and pick one up no problem. My buttons are OK with me reaching in their cage but if I try to pick one up its like someone pulled the fire alarm and they scatter. A lot of the people on here generally have at least double digits in quail so it's not feasible for them to keep them inside it's totally doable with a small group tho with only three or four girls and a boy or just a couple of girls.