I am SO sorry! It's so hard to lose them, especially when we get so attached. As far as your neighbors go, it's hard being the new kid on the block and have to approach someone with an issue like that. I know exactly how that feels ... absolutely exactly. Way back when, I had to do the same thing when a neighbor's dog was caught red handed tearing my (sturdy!) rabbit hutches apart ... the very night we moved in. She got my favorite doe, who had three kits too small to hand rear, and another who was already pulling hair to kindle.I'm not sure, as we are still pretty new here. We wanted to run over and talk to the neighbors, but being in farmland here... There are farm cats all over the place. If theirs didn't do it, someone else's would. It's a good reminder how important it is to have a super secure run. We are heartbroken though, as he was the sweetest guy. He was always the first out to say "hi". He followed me around in the coop and run.
I'm considering talking to our animal control and see what they recommend.
I think you've got the right attitude about it, though. It's time to reinforce the run, and maybe leave a little electric surprise around the sides. There's an old adage that rings very true:
A cat will sit on a hot stove once ... then never again on a cold one.
Make it unpleasant enough for Kitty, and he won't be back!