Excellent history and information, thank you.
I think you have handled this perfectly, your honourary vet degree is in the mail :)
I expect this is exactly what your vet is saying...a case of contact or air borne allergies, and not from the shampoo.
Speak to your veterinarian about omega fatty acids or other dietary supplements that can help reduce the itchiness. you may also want to steam clean the carpets in your new home, perhaps they have been shampooed with something irritating to your pet's fur.