I have an EE hen like that and similar to you, live in a high density population area. She screams a lot for the sake of screaming, it seems. It is who she is, yes, but since I'd like to keep her, I'm trying to modify her behavior. First, I try not to feed her treats directly, rather leave things in the run and the coop when they're not looking. And they never, ever get treats or let out into the larger yard if they're being noisy.
And finally, when she's being super duper jerky, she gets sprayed with the hose. Not soaked, but splashed, and shuts her up for a long while. To note, I never do this for the actual "egg song," just for the nonsense demand bwaks. It'd be nice if this curbed her loudmouthed tendencies altogether. She's gotten a lot better, but still has her moments.
As for the egg songs and other ambient noise they make, as long as it's within construction hours, I've had to learn to not care as much. Dogs bark, cars go by continually, kids are screaming and the chickens just add their $.02 to the mix. Crack of dawn on a Sunday morning, on the other hand...