I'd make sure I fed a food w/o corn, wheat or soy, that had most of its protein from animal sources (so a high quality food = $$), or raw. To that I would add high quality fish oil for a daily dose of 1000 mg of omega 3 fats. For the Sealogix brand I use (pharmaceutical grade supplement = $$), that's 1/2 tsp a day (total), which I divide into two 1/4 tspn doses since I feed morning and evening. In your place, I would also add 2 tspns of high quality olive oil (I use Napoleon Extra Virgin) per meal, ASSUMING 2x day feedings.
Sometimes just adding some good fats kills the itching, assuming it's not flea allergy (less likely in your cold clime, unless your house has them). If you notice the stools getting too soft, back off the olive oil a bit - too much fat will cause that. Assuming the itching stops, you could try backing out the olive oil (assuming you wanted to), but I'd not reduce or stop the fish oil since it's so good for them (and you).
I'd also stop bathing the dog to allow a neutral pH to do its work, and I'd groom daily with a shorter-toothed rake to remove old hair and to move skin oils up onto the coat. My dogs (one is a GSD w/hx of itching) look and feel great. Best of luck working it out.