I would make an appointment with a specialist (asap) either veterinary internal medicine or a veterinary dermatologist for testing/diagnosis/treatment. Sounds like environmental allergies could be the culprit and not the food.
Ask your vet to refer you. Prednisone is not good long term and can lead to other health issues, he has not responded to diet changes.
Enough is enough.
PS: There is no miracle food that will fix this.
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