What type of allergy testing was done?
PS: Because if one were to believe the results you have presented. There is no commercial dog food that will meet your criteria. Cross contamination and all.
You would either have to go with prescription/therapeutic food or consult a veterinarian that specializes in nutrition.
Not the internet.
Food allergies are rare and food sensitivities tend to fluctuate. I would consider consulting a veterinary dermatologist for a second opinion, intradermal skin testing (the most accurate way to identify environmental allergens).
Good luck
