Stop being so involved in their business? Forgive me, but that is just silly. How comfortable would you be, sitting and listening to a little bird being torn apart at night by dogs? I would not be able to sit still for that, and if I tried, I would not be able to rest, and it would haunt me the next day. Also, what if some of their birds come over the fence, and the OP's birds catch mites or other things from them?
I don't think the neighbor's birds are necessarily used for egg production alone, as it sounds like they tend to go missing around holidays.
The next time you are awakened by the neighbor's dogs terrorizing their birds, go over to their front door and bang loudly on it. Look very concerned, and tell them earnestly that something is trying to tear apart some of their birds. Tell them that you fear for your own birds, and that you can hear it, and came over to tell them rather than call the police. Offer to go back there with your frying pan, gun, nunchucks, whatever, to help them ward off the wolves, coyotes, bears, etc. If you make enough of an earnest performance, I think they will take the hint, without getting angry. If this does not help, you can hide a bird, and call animal control.
In the meantime, seeing if their son would like help constructing a proper coop would be a really nice idea. (You could certainly tell him that the birds would be much safer, and grow much better if they are not continually stressed). He also may like the idea of making their yard nicer, and more garden-like, like yours.
Good luck, let us know what happens, and I hope that the situation improves.