We just want to finish up our lease here and find another place to live. When we're quit of this place, we're quit of him and that's life.
One of my favourite quotes from the Art of War is "
he who has an enemy shall suffer"
It is one of the most misunderstood quotes and more commonly interpreted as meaning "if you decide to make an enemy out of somone then you will suffer".
But as in this instance you have an enemy and you are sufferring and will continue to suffer until this enemy is eliminated. It is not your fault you have the enemy, you didn't choose him, he chose you.
I can appreciate you are happy to move house but if you hoarde anything like I do then it will cost over $1,000 to move all your stuff, then you have the effort involved, the inconvenience and potential problems at the new place anyway.
I wish I knew a great way to eliminate these sorts of enemies but i don't..no amount of compliance will work, Military strikes are probably not the order of the day, escalation may cause him to back down but it may make things worse, eliminating his ability to cause you harm is difficult, potentially risky and expensive(keep doing things that irritate him until the local departments regard him as no more than a prank caller).
Just beating someone into submission is not enough since they may still think they have a chance so it is not enough to just win but you have to make sure they
know they can not win. In your case you need at least three entities to tell him so. The Sherriff's office and Animal control need to tell him to stop calling them and the local courts need to tell him not to waste their time(since that would probably be his next step).
Since moving won't necessarily fix your problem because you may get a neighbour ten times worse at the new place and therefore still have to find a real solution I would recommend trying a little harder to eliminate this person as an enemy. Which doesn't mean leave him with a pair of concrete boots at the bottom of the river. I'm not saying make him your friend either, you just have to make him no longer be your enemy.
First thing to realise is this guy has problems and as far as he is concerned, they are really big problems and you are just the last straw. So spy on him a little, do a little social engineering, get inside his space and find out what his problems are. Odds are his wife is a cow, she treats him like garbage, the baby just won't shut up, he's sad because he is a complete and utter wimp, he can't fight, lived with his mom so long he has lost all touch with his manhood and to top it all off the "tuff-guy" living next door who has the whole world in the palm of his hand is scary cause mommy never taught him how to be a man.
Bearing all of this in mind, ask him for a favour...ask him to help you hang the punching bag which is too heavy to do on your own(not) and teach him some Karate. Teach this tosser that as much as he may hate the bogey man living next door he needs you.