Before a hen starts laying she builds up excess fat. If you butcher pullets, hens, cockerels, and roosters you can clearly see the difference. That excess fat is what they mostly live off of while broody so they can take care of the eggs instead of needing to search for food and water. They...
I've had as many as three broodies together in my 3' x 6' brooder. They all broke. But like anything else I'd be nervous if they were packed in tight. It depends on the size of the pen.
I'd increase the lip on those nests another three inches or so to keep the bedding in and then add a few inches of bedding. You do not have to shape that bedding, they will do that for themselves. I'd do that even just for laying eggs, let alone incubating or hatching. With the lip that low...