I have seen a few horrible cases of SA in Poodles, but more commonly Akitas. Unfortunately, food changes don't make a significant difference. Feeding a diet high in fat/oils is better than something higher in carbs.
Raw diets are actually not recommended by most specialists with dogs dealing with SA, as the body is compromised any natural bacterias which most dogs can tolerate, may not be tolerable by these dogs. Home cooked food is a better option for these ones, or commercial kibbles that suit your dogs dietary requirements. Adding fish oil can help too.
What medication has your pup been on? Typically, we treat SA in two ways medically - cyclosporine, or prednisone. There is also an important shampoo/oil bath that in combination with medical therapy is very helpful.
If you can, seek out a consult with a boarded dermatologist. The consult fees arent as expensive as you think (probably $150-200), and they can give you the names/dosages of drugs that you can get through them or your regular vet, plus the names/directions of use for shampoos and oil soaks.
I would think if you can invest $5-600 into this dog (specialist consult, meds, bathing, bloodwork), you will be able to significantly improve her quality of life, or at least give yourself peace of mind that you have done everything possible to give her a chance.
Sounds like she has been a very lucky dog to have found you