Baking soda is amazing for odor. I have used it under the bedding in a duckling brooder and can hardly smell the ducklings from a foot away (and trust me, nothing is stankier than a brooder full of ducklings--if you think quail smell bad, you haven't ever shared a workspace with a duckling).
But for best results, put the baking soda where the smell is--not just in an open box. Actually sprinkle it, liberally, into the tray under your quail. Don't put it where they will walk in it, as it is alkaline and abrasive and can be irritating over time (though it is also totally non-toxic just like DE) to their feet. If they are on wire, put it on a surface below the wire or, if they are on bedding, sprinkle it in the bottom of the tray and then put the bedding on top.
You will be amazed how much odor it will absorb.
Good luck. Coturnix actually make very cool little indoor pets. We keep one (he was hatched alone--long story--and is afraid of other quail) in a bird cage in the living room. Alone, he's no stinkier than any other domestic bird--we just keep the cage clean and use baking soda in the tray. He's very friendly and calm--lets our children carry him all over the house and chills in his sandbox most of the day, alternately napping and crowing at us when we come into the room. Quite a conversation starter, too.
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.
Use pine pellets instead of pine shavings, it absorbs wetness and odor much better than pellets. Plus it smells better, and when it gets wet it releases a pine smell, until it gets really nasty anyway. Other than that, there's not much you can do.