I've never worked with Bobwhites, so I can't say what they would do. With chickens, which I have worked with broody hens for the last 10 years, it would really depend on the hen. Typically you want to move the hen way before hatching starts to avoid disrupting air cells in the eggs or malpositioning a chick.
However, I do agree it doesn't sound like a good set up. I have successfully open coop hatched with broodies (one year I had 3 co-brood successfully). And then there were years it was an utter disaster with chicks being kicked out of the nest by other birds or stepped on and crushed. The solution has always been having the broody in an isolated coop. Some can co-brood with another in that coop. Others have to be alone or there is trouble.
If the eggs weren't set at the same time, you are also struggling with a staggered hatch which means chicks hatching over a number of days. This can cause issues as many moms stay with the unhatched eggs and don't tend to the new babes. The solution to this is always set eggs at the same time so that the babes are hatching over a 24 hour period (in chickens).
Depending on the desperation of the situation, you might want to try to move the hens and clutches. However, in chickens, it totally depends on the hen whether she WILL move. Some become very upset and abandon the eggs as they are attached to the original nest location. Again, I would, with chickens, be very hesitant to move hatching eggs. You don't need a hen upset and unsettled during this delicate phase.
But....if this indeed is times of desperation and you sense a disaster about to happen, you can definitely try moving the mommas to a quiet, dark, isolation nest crossing your fingers you don't disturb chicks in the eggs, cause a shrink wrap from a cracked egg (losing humidity with move), or creating an upset hen who won't settle.
Hopefully others who have direct experience with Bobwhites will reply.
LofMc
