@Red.Rooster My (hospital worker) wife says she has seen people with undiagnosed liver diseases have uncontrollable itching. I know it can also be a side effect of diabetes, but I assume ordinary blood tests would have shown that.
I did a couple hours of research today trying to ferret something out that you might not have considered. It is depressingly astounding how many people on the Internet report this ailment and state they have not yet found a solution.
Some suggestions synthesized from this reading that your doctors might have already suggested, but you never know:
First, think back to one month to six weeks before it started. Any changes in a) diet; b) soap or laundry detergent (a change to Borax once caused me to erupt like crazy, now we use unscented All, a lifesaver); c) water chemistry, esp water softener if on a well (or any chance of chemical pollution) or home filtration, or bottled beverage intake; d) fabrics worn or bed linens or towels; e) pesticides inside or outside your home; f) vitamins or other medications; g) pets or pet behavior, even fleas or use of a flea collar; or h) a/c or furnace filters or buildup of dust anywhere in the house or car? Finally, any change in the temperature you keep at home?
Second, I assume you have considered scabies and or bed bugs?
Third, these things are often related to allergies or auto-immune issues. Sometimes people respond to a mild allergy or itchiness by taking antihistamines such Benadry, but those actually work by suppressing your body's immune system, and a side effect can be to dry out your tissues including the skin. Steroid/cortison use can sometimes relieve the itching, but it might conversely worsen it.
Fourth, does your wife's condition make her feel hot or burning, or cause unexplained sweating? You might see if lowering your house temperature 3 or 4 degrees brings some relief, or even more at night. Several people have reported that this made a difference, and I saw some speculation that people can develop allergies to their own sweating.
Fifth, check out any local businesses or industrial plants that might be nearby (perhaps a local environmental services agency or group) to see if any have been reported for releasing any chemicals, or if other people have also reported similar unexplained problems. You never know.
Anyway, these are just some ideas that cropped up. My heart goes out to both of you. It could be something external, but if not, I hope you have a chance to see a good neurologist if a dermatologist cannot find the answer. Liver issues would involved a hepatologist. Make any doctor you consult try to find an answer. Consider a research hospital if necessary.
Good luck. As you know, I am not a doctor, but I believe sometimes collective knowledge sharing among laymen can help doctors find some answers.
Edit: my parenthetical (letter bee) in the list above created an unintentional sunglasses emoji. Sorry about that.