Poor you! I had a horrible neighbor who terrorized us--I knew it was her because it started after she moved in, and ended when she left. Psycho....and she babysat other people's kids...
Then some renters moved into another house and stole the entire wheel, and lug nuts off my car. No way to prove it was them. That's when I spent some money on a four camera system with a dvr. It is awesome, and has ir for nighttime, although it doesn't see far enough at night so we put up the energy saving bulb spot lights pointing into the dark spots by the cars. I love having them because DH was working nights and if something made a weird noise I could turn on the tv and see what was going on outside.
We have them visible, and I believe they are a real deterrent to people with ill intent.
It sounds to me as if your neighbor is doing things on purpose to allow and entice your birds into his yard now. What kind of fence do you have on the border with him? Did you examine the new hole to see if maybe he helped it along? Was there any sign of a trail that your animals were using it for any time?
And if he is doing things to harass your birds when they are on your property, he is probably breaking the law, so if it were me, I would really want to see what goes on when I'm not home... If you can't put out money for cameras, perhaps you could pretend to go to work as usual, but sneak home and hide out with a camera.
The guy now has a bee in his bonnet and I'm thinking he will not relent...just like my psycho lady...maybe they are related