A friend of mine took her dog to a vet dermatologist today and got
a diagnosis on the first visit. Among many diagnostic tests done, a
fur culture turned up positive for a bacterial infection (which
wasn't even done during all of Shamrock's diagnostics, and I never
knew that test existed).  Apparently a bacterial infection can
arise from inhalant allergies like dust, mold, pollen. The
treatment for her dog is a month-long antibiotic course and bathing
just the affected area with a special shampoo, thus not bathing the
whole animal.

Even if a culture of Shamrock's fur is negative for bacterial
infection, this vet does intradermal allergy testing and if one of
the common inhalent (and whatever else they test for) allergens is
positive, they have great results for cats in particular by using
hyposensitization injections that can be done at home. But, it
looks like the first line of defense is to eliminate the allergen,
if possible. It isn't always possible, though.

From their web site on the "allergy" page:
"The cost of allergy testing animals is a fraction of the cost of
human allergy testing, even though the same allergens and expertise
are employed. The allergy injection program, called
hyposensitization, is effective in 75-80 percent of dogs, and 85-90
percent of cats."
http://www.animalskindisease.com

Encouraging!!  Wish us luck for this poor cat of mine who's been
affected for all of the 3 years he's been here with me!