Forgot to mention about the electric fence, go with the plain smooth wire, barbed wire is not needed, the shock is what does the trick not the wire, also in some areas electrifying barbed wire is illegal as a person or animal could potentially get snagged on it and not be able to escape the shock as quickly. I don't know if they have any such law in your area but it just isn't necessary. Smooth wire is likely cheaper as well and you won't constantly be snagging and poking yourself when you work with it or around it.
I know what you mean about getting so mad you would beat the daylights out of the dogs for going after your birds, I am to the point with my jerk neighbor that I am done with law enforcement measures and any of his dogs that are on my property and harassing my chickens or my dogs will be shot on sight, that is legal and considered acceptable by most standards in my area, however beating a dog senseless can lead to all kinds of animal abuse/cruelty allegations, lawsuits, possible fines or jail time, even if you are justified in doing so, so if you can't use lethal force to protect your birds it is a fine line you are walking if you take other measures, though in my eyes if they are attacking all bets are off, beat them to death if you must.
It sounds like your neighbors are down right inconsiderate about the birds, but you can't really fault them for allowing the dogs in their own back yard if in fact the dogs are staying in THEIR backyard and not crossing into yours, I would put that electric fence about 1 inch on your side of the property line all along your property line with them, I doubt they will enjoy the fact that they now have to have an electrified fence bordering their yard due to their stubbornness at refusing to remedy the situation, I too would grease the wires to entice the dogs to lick it and get a good zap, it would likely make them stay far away, if it did draw in another animal they would get the same education in a hurry and likely not return. I would continue with the reports to the animal control agency or police dept as well, they usually are required to look into every single complaint and sooner or later they will be forced to act as they will get tired of responding.