Chickens in a box- lockdown!

Since the most determined little brown hen got up off her eggs for the second time, right before they were due, toasting another clutch, I finally listened to HW and removed her from the coop and locked her up.  This is her third nearly-complete round, and that's a long time for her to be sitting and mostly not eating.Another brown hen went broody at the same time, and I got to them just in time, as each already had an eight egg horde- a little ambitious, but it's summer, so I let them keep all eight.  Now they are boxed.HW and I went back and forth- I have had bad luck when I interfere with them, but it has also not gone well when I don't interfere with them.  They find ways to screw up; it's very frustrating.  He told me "just take them out of the coop entirely, then there's no distractions, no more eggs to steal".  This means I will have to reintroduce them to the flock, and learning how to go in and out of the coop may be that much harder, but we'll cross that hurdle once we get some chicks, I suppose.They are in ventilated boxes next to the door of the greenhouse.  I'm a bit paranoid of them getting too hot in there, and how secure are they in the GH at night?, but so far, so good.  There is always a healthy cooling  draft through the GH.  They each have a fount with their poultry vitamin supplement (chicken Gatorade), and a little bowl of food, which they both consume a little of every day, I'm glad, and I sometimes have to scoop their poop.There are four more sister hens and the original white hen (outside), who is a little old lady now.  She seems to have shrunk, so tiny when you pick her up.  Still cranky though.  If any more drop into the broody trance, I'm going to have a whole lineup of bird boxes.