Are you sure that screeching is not just an egg song, or escort call? My girls can be quite noisy in the nest box, and then Pippi joins in with them.It can get quite noisy around here.
Well the video is at the wrong angle, but it’s the Brahma, Buttercup who screeches here. I took the egg, took her out, dipped her legs (she actually likes it) and she was done with it. Does this seem like a broody screech to you?