You are correct about broodiness. Broody hens will "borrow" any eggs laid by other chickens, hence the need to keep removing eggs from under them. The broodies themselves aren't laying while in the zone.
Huh, well, I guess this demonstrates the variability among breeds. My two hens prone to broodiness always kept laying. Yes, they'd borrow eggs from the other layers but they'd also lay one of their own eggs every day.
For days, even weeks in a row, I remove the eggs from under her and she eventually leaves the nest, only to return the next morning to repeat. She'd like to keep those eggs, her whole demeanor has changed and I have to ward off pecks when I get the eggs, but, so long as I remove them she doesn't go into the deep trance of broodiness.
Then, when I want her to start a clutch I stop removing the eggs. At that point she does quit laying and within a couple days she's deep in her trance.
My point is that I've never had a bird going into deep broodiness on an empty nest. I think it'd be time to cull any bird that would sit on an empty nest and not lay.