This is a puzzle, the two main features that strike me are pain and vomiting.
Frequently diagnostic tests do not come back with the answer, and I always ask myself, "Is this test really negative/positive, or is it just a false result?",and "What other tests can I run to seek out the answer?"
It is always important to look at the history of the patient and then do the physical exam--serially if need be. There is something painful that is causing your cat to starve itself, it is crying out for food, but the pain is worse than the hunger.
I would focus on the mouth (potentionally there could be some deep soft tissue reason such as a tumor, sinus infection, unerupted/impacted/broken root tooth problem, temporal mandibular joint problems, esophagitis secondary to reflux/hiatial hernia/diaphragmatic hernia, pyloric disease, and so on. If I was working this case up, I would do dental x-rays, a skull MRI (rules-out tumors/sinusitis/TMJ/, endoscopy to examine the esophagus /stomach/pylorus for various disorders/damage/foreign bodies/masses.
Certainly certain dietary deficiencies could be at play here also, given the diet heavy in a single ingredient.
If I was absolutely at a dead-end because of finances/lack of testing, then I would put your kitty on a course of glucocorticoids, antibiotics, proton ion pump inhibitors (Nexium), sulcrafate and potentionally a narcotic.
Nevertheless I would prefer to actually have a diagnosis before doing symptomatic treatment.
We do what we must under circumstances, we do not live in a perfect world.
I hope this helps.
Dr. Van Lienden
Dr. Raymond Van Lienden DVM
The Animal Clinic of Clifton
12702 Chapel Road, Clifton
Virginia, U.S.A. 20124