That was a bizarre initial presentation. At present, if it's just the skin, then given the 'dependency' on pred, the facial inflammation and the use of a processed food, I would target the Spleen and Dampness first. It's Spleen deficiency that leads to vacuities (e.g., of Blood) that allow easy Wind invasion.
To make a stab in that direction, I'd be tempted to try Si Miao San (Four Marvels). Even if it doesn't eradicate the problem, it may greatly reduce the required dose of pred to keep the cat symptom-free. If it does work, then you know that the diet is the culprit
The alternate approach is to use Minor Bupleurum (Xiao Chai Hu Tang) on the assumption that the initial presentation was one of immune mediated disease that included a mitogenc response (i.e., lymphocytosis) and even a blood dyscrasia. Minor Bupleurum treats Shao Yang disharmony. Shao Yang disharmony is associated with excess systemic immune reactions. In Chinese medical terms, it is commonly associated with the entrapment of Yang in the Yang Ming, which can reflect itself in facial inflammation.
One of those two approaches should work. I guess I would be tempted to try Minor Bupleurum first.
Hope this helps!