I've had personal experience with the evil neighbor type that is harrassing you. IF you get rid of the roos, then he will decide the hens are too smelly, dusty, dirty, rat and predator lures etc. He just has it in for you and nothing is going to satisfy him. I'm guessing he doesn't have a dog so you could complain about that. But he must do something, loud boombox, lawn mower, weed whacker,wild parties, something = maybe tinkers with his car long and loudly. YOu HAVE to find something - his weak spot, bullies hate it when you fight back.
Having said that, I'd keep my chickens locked up safely, and anything else you think he'd bother for spite. Could you move your coop to a site farther from him? Have you ever seen what his property looks like on the otherside of the 6 ft. fence. Send someone up on a ladder to check it out. Maybe you can find some violation in his yard. If you can afford it get motion detector and a game cam to alert you to anyone trespassing on your property - namely him.
Naperville is beautiful and huge, he can find somewhere else to live = maybe some cave. I'm in Willow Springs, my brother in Downers Grove, so we aren't terribly far from you. I used to go to a dentist in Naperville., and Jason's Deli (before they opened some nearer to us). I think it's fantastic that they allow chickens and it's just too darn bad for him. My friend in Countryside, near LaGrange, has been looking for bantams but she wants silkied seramas. But please don't give up your happiness for him, he will never be happy - trust me.