Jennie,
I'm concerned the guy has a mental health problem. He's spirling down and showing his depression as agression.
I think you need to stop worrying about the power struggle
He's completely trapped in it, looking for some small place he can be the big man since he has lost everything.
You need to look at him as handicapped, not an equal and not a rival. If you saw him as handicapped and not quite in his right mind, how would you change how you are dealing with him?
Do not make yourself his target. Cool the problems between you as best you can.
Take the highest road you can.
If his wife is your best friend, do it for her and your chickens. The more this guy escalates, the more dangerous he becomes in my mind.
I would treat him with concern, not anger.
Any threats would be documented and reported.
I would tell the cops that he is looking like he is getting really depressed and aggressive if this keeps up.
I encourage you to look for ways to do what you call 'backing down' since this is a silly fight to start with. I do want to say, he's been ugly to you. He's a master at getting under people's skin. But you are rewarding him by letting it bother you and escalate. It makes him feel powerful. The longer he can keep it going, keep you upset, the more powerful he feels. It's pathetic. And since he is a master, you like many of us would, fell into his trap. You have to get out of it. He is too sick to end this. You have to.
I might say something like, I think I over-reacted to your first email and I'm sorry I did that. I'm sorry for my part on letting this get out of hand. I will do everything I can to keep my chickens out of your yard and not bothering you. Let's stop this stuff now. I know you are a better man than this as well.
I know you won't want to say that but I'm worried he will go postal at some point. And you don't want to be a target of it. It costs you nothing to take the high road. This is not a person you need to have an honest to goodness, good feeling, glad he likes me and we worked that out moment with. You just need to stop him perseverating about you. Find a way to do it as a strategy for peace. We don't care that he is an a$$. Just understand he's handicapped.
I think the preacher would join me in saying the best thing you can do is to start praying for him. The guy is in trouble. Maybe he will just keep being nasty and depressed. But this is also the profile of someone who gives up and goes postal.