All, I introduced the chickens to the thread to see what the reactions would be. I did so for two purposes, one, they are considered not as dangerous as dogs, two, the basic issue is the same.
The issue is the neighbor will not control the animals. I believe some people, you just cannot talk with, they don't get it. In this instance the original poster has tried communication and collaborative efforts to offer a controlled manner in which to contain the issue. However, the neighbor just does not see anything basically wrong with the behaviour of his animals. They cannot think "what if?".
I would offer this. Under no circumstance would I spend money to fix this issue with material. I would send a registered letter to the neighbor and local animal control, perhaps even the local LEO. I would then wait, and see if the issue has been taken care of. If not, I would call animal control and the LEO out and have them observe the behavior. If that is not possible, well others have stated some more choices.
In my case, the chickens are an issue. My neighbor refuses to contain them, I have tried communicating with him, but he is a very angry person. IMHO. It has not come down to a registered letter yet. Nor will it. As he stated to me ...this is the country, get use to it. IMHO, this offers numerous possibilities.