Kevin, you win big points for effort. And I'm sure I'm not alone in appreciating how willing you are to enlist criticism, and actually move in a different direction when it's pointed out as being necessary.
But.
I'm afraid you need to sit down and close your eyes and pretend you are a baby chick in a group of other baby chicks and baby quail. Would you be happy in a box all enclosed and not be able to see out? Or be able to see who's coming? Or be able to see nothing else but a big, giant hand coming at you from no where?
The big box is a great start. I would get the saber saw out and cut nice big windows in the sides. You can cover them with see-through plastic, or install glass as long as you seem to be good at building stuff. Then build a platform for the brooder and get it up off the floor. You will need to have a great deal of open area over the top to keep the heat from the heat lamp from building up like an oven and cooking the babies. I'd cut some skylights and cover them with netting or hardware cloth.
If you have the brooder up on legs so you are administering to the babies from the side, and they can see a human is attached to the big hand and not a predator, you will be raising a batch of the friendliest chicks imaginable.
I don't see why quail can't safely have pine shavings also. If there is something to that prohibition, peat moss works as good as pine shavings, and they'll love dust bathing in it. Or you can use sand.