I'm starting a similar journey with my 15 month pup. She's needed a short course of steroids, which immediately stopped her scratching but after a month and coincidentally a day after her immunisation jab, she returned to full on scratching and foot nibbling. Then a course of Apolquel, completed 2 weeks ago. At the moment she has slight irritation, so occasionally biting feet but her belly and chest skin are good.
I'm so hoping she grows out of this but one of the vets has mentioned that most dogs don't or even get worse.
I suspect that for Greta some of her problems are environmental, grass pollen/seeds. I have also removed chicken from her diet. Another vet advised this as often it is identified as an allergen for many dogs. The first episode of allergies was when she was on chicken, the second was during pollen season. But to be honest she has been bothered since 7 weeks old, I asked the breeder about it but she replied that the pup had been fine with her.
I plan to do the blood testing when there is less produce about the garden as Greta is a persistent forager. Her diet needs to be totally limited for accuracy with the testing.
It's a frustrating situation so I have great empathy for you and your V. Good luck with findings answers. I'm also thinking of asking for a specialist vet referral for this condition, I have insurance!!