What a nightmare you've endured! Where I live (NY), any dog that has bitten someone is automatically quarantined for ten days and the owner must provide proof that the dog has been vaccinated against Rabies. If the dog bites someone three times, it is euthanized.
Insurance companies raise the premiums on homes with dogs that are considered to be dangerous. Rhodesian Ridgebacks are beautiful dogs, but they are bred to chase large game and to protect their owners. Again, the parentage can make a large difference in how the dog behaves (or not)!
It would be difficult to set a trap for a Ridgeback because of their tremendous size and power.
The Jack Russell would be easier to trap. However, I once read in a dog magazine that this particular breed was known as the "Anti-Christ". No flames please. My ex-husband had one and this dog was stubborn, stubborn, stubborn.
Once there was a large Rottweiler that came onto my property and started growling at the Jack Russell after I had returned home with the dog. Of course, the little dog starts yapping away as if she could hurt him. The Rottweiler had that look in his eyes, an aggressive, scary look. I summoned up my firmest voice and yelled, "No! Go home! Go!" while pointing with my finger. My ex picked up the Jack Russell and threw it on top of my car. Now the car was all scratched up. The Rottweiler kept circling the car trying to get at the Jack. I threw a full bottle of Snapple Ice Tea at the Rott. It bounced off of him and he didn't even feel it! I started beating the dog repeatedly with my purse and that didn't help. My ex brought the Jack inside and I called the police. A cruiser showed up after 15 minutes but the officers wouldn't get out of the car! I showed them where the dog lived but they were too scared! I thought that if they knew that there was an aggressive dog, they'd come with a tranquiler, but they didn't. I don't know why they bothered coming out at all. I waited and waited until the owners came home. They apologized profusely and offered to pay for any damages. (Their dog was vaccinated.) I forgot to mention the scratches on the roof of my car. Darn!
On the flip side, I had a neighbor who knew my male Rottweiler since my dog was a puppy. The neighbor would come over to dogsit on occassion and I would return the favor by buying sod for him, planting it, and making him food. One day I found out that he had filed a claim with my insurance company claiming that my dog had bit hiim! I had erected a 6' high chain link fence between the two properties. There was no way that the neighbor could have been bitten unless he had stuck his finger through the fence.
As a result, the "neighbor" received a $10,000 check from my homeowner's policy even though I offered pictures of the property to show that he couldn't have been bitten without sticking his fingers through the fence. My homeowners' policy went up. By the way, my dog had never been loose, was trained to obey hand commands and the like.
You're in a very difficult situation. I can fully understand that it's hard to deal with irrational people. Perhaps you can really, really, really lean on the police and animal control. Everyone has a boss. Make the waves and make them big. Don't let up. You don't have to hurt the dogs but you don't have to deal with this nonsense either, if you're persistent.
Good luck!
Suzy