If he’s flying over your fence, maybe you could try catching him and clipping his wings? I don’t know your neighborhood or how people feel about the neighbor’s chickens coming into their yard. I know that where I live, it’s considered common courtesy to keep your animals on your own property. You mentioned the potential of your chickens ending up at your neighbor’s house - I’d work really hard not to let that happen no matter how you resolve the rooster problem. You relocate him, what’s to stop your neighbor from doing the same with your birds if they wander?