I had the opposite, my friend gave me her broody speckled Sussex which she did nothing about. She got to me and I never seen her broody for a second 🤷♀️🐓❤️
Based on all my reading, Looks like your setup is spot on. I have never had a broody hen, but if I did, her set up would look the same as yours. Good luck! 🐓❤️