Sorry to hear of the issues! But I've had button quail for a bit and I moved them to a large pen not long after I got them - and what I did was put the first pen in the larger pen for a day or two - then opened the door to it and let them 'explore' at their will... I would try that and see how they do. Also - I would try tacking some aviary netting (deer netting/bird netting you can get at SS or TSC) and have it be a little loose and a foot from the top , this way if they do go to bouncing and flying they wouldn't hit anything hard and unforgiving with their heads.
You did a great job BTW - I love the pens!!! I had helped my friend make something similar once for her iguana but it was no where near as cute as yours are!
those look like good cages, just pull the roof and swap it with mesh, or fabric. Quail do fine in small cages, but they definitely appreciate more space.