Reading things like this makes me so glad I have good neighbors. I have 2 neighbors. 1 hardly ever comes outside, she's a couch potato that has no issue what so ever with my birds. She even finds them cute. And my other is an old elderly woman that sits on her porch on good weather'ed days. She cant even hear my birds she's so far from our house. I think she can hardly hear someone sitting next to her talk actually lol. Either way I feel lucky when reading these types of threads.
My best advice to you is that you should play dirty like he is. Since the birds are gonna die anyways, break one's neck, and break one of your own windows on the house. Then call the cops and tell them that he was shooting at your house, shot out a window and shot a bird. Seriously, some times you have to do poop like that to get anything done by the cops.