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That totally makes sense about the lack of cat role models to teach proper behavior. (So if this cat is modeling your behavior, how scary are you and your spouse?)
After three years, cats don't adapt easily to change. But Cary is headed in the right direction.
Consulting a cat behavior expert is a great idea. You might also consider whether there is a veterinary college nearby where students might study and evaluate your cat, or for a small bribe accidentally have it end up in the disection lab (just kidding!!!) Seriously, the cat could be a great behavioral case study.
You can try a dog crate/kennel large enough for the cat and litter box. Cats sleep most of the day, so being in a crate could provide a safe territory for the cat to protect without terrorizing the entire house. A cover might be calming as well.
You can try cat videos on your television, much safer than exposing a real companion to FrankenKitty. Maybe by modeling cat behavior, the videos might calm the cat. (Use an old television in case it just enrages your little critter and it claws the screen.) My cat really loves watching other cats on my computer screen, then looks around back of the laptop to find out where they're hiding.
You can find a "cat lady." If she has 100 cats, she might be happy to take one more and it could thin the herd, doing her a favor. (Kidding again, couldn't resist).
If that doesn't work, try an extension office or co-op or some other organization that works with farmers or rural residents. It is not right to dump a cat on a rural road, but there may be some animal rescue program that could help find a home that could use a very aggressive cat to keep mice and rats out of the barn.
In the end, I do not feel that putting the animal down is morally weak, if the cat is suffering from its inability to bond with anyone or anything. This is not a good life for you or it.
I had a friend who let a girlfriend move in -- and celebrate the event with a new cat. The girlfriend left three weeks later and my friend ended up with a psychotic cat for 24 YEARS. Every time he got on the phone the cat screamed. Whenever he invited anyone over, the cat turned into a tiny cougar. My friend has Asperger's, so the lack of human companionship and the cat's lack of affection worked out OK, but it sounds like you need a life.
Humane society or animal rescue folks can help you through this. They are very level-headed about when cats can and can't be saved, and it has more to do with behavior than physical health.
Do your level best. That's all you can do... and remember, without you the cat would have died three years ago.