If I were you I would put them in a nice sized rabbit cage like this:
& put about 2" or so of colorless playsand mixed with DE in the tray, you can then scoop it with a fine mesh scooper like this:
& scoop it daily, also they will enjoy the dust baths & aslong as you don't put that much sand in the tray they won't be able to hide the eggs ect.
If you have them in wire bottom cages you could also just put the sand & DE mix in there. but also make sure you take a scrub brush to the wire floor daily to scrape away any poop that is stuck to it.
The sand clumps up like cat litter, but is safe if they ate small bits of it & The DE is also safe to eat & will help to dry the terds out & therefore help the clumping of it all.
I used to do this with my indoor pet/breeding quail, all 200 or so of them, just have a small handheld vacuum ready for the big weekly cleaning day...it makes life so much easier!
I never had any smell problems with the quail, but I also had a air filter & kept the humidity & temperature fairly low.
I still would be wary though of using sand in out door runs, sounds like it would be just as good, but in the sun sand can get very hot.