annaraven, you sound like a very kind and compassionate person. i have done some trapping and feral fixing in my time, and some rehabbing. It is hard work, time consuming, costly, and pretty thankless. So anyone who takes on that challenge should be commended.
You know, it's such a delicate balance, because i am very compassionate towards those that choose to let their cats outside. i think most cats would love to be out exploring. i would actually love to set up a secure area so my cats can be outside. A friend of mind put together a kennel outside their house. Their cats go out the window and can be in the grass and sunshine, but still protected. She had to do this as one of her cats has feline aids and can't risk getting in a fight and injured.
i don't know what to do at this point. i had suggested to them installing hardware cloth on the fence between our houses so the cat would have a very difficult time climbing over. If he had to come from another direction, the goats would see him and intercept. Perhaps we can try this and see if it solves the problem.