I haven't had any go super broody in the flight cage yet, they seem to share the best spots for laying (the hollow logs and the small dog house) and I think that discourages them somewhat. This year I have seen 4 separate broods of baby quail in the area from my released adults so they are making it and propagating on their own.
I've had problems with squirrels chewing holes in the netting and then some of the quail escape, but it has turned out to be an inadvertent way to acclimate them to the wild. When I feed the quail I often leave the door open and I've often had the escapees jump back into the flight cage after having a few days or a week of freedom. This happens especially in the fall and winter when they want to be in a covey. The end result is they get experience being on their own, trying new foods and learning about predators.
In late spring after collecting eggs for a month or so, I keep 100 eggs for incubation and let the adults loose to re-propagate the area.