Yes, you did indeed state Cookie is a male. My bad! Cookie just sounded like a girl name to me, but my first cat (a female) was named Harvey.
I did some research on VIN, veterinarian information network, a website of veterinary specialists, about phage therapy in cats. I found some promising new research being done with people and resistant infections, but the only references I could find for cats was still in the experimental phases, or for using using Staph Phage Lysate (SPL) therapy as an immune stimulant.
Was a culture done, is that how it was determined this is Pseudomonas aeruginosa? If so, did you get a sensitivity report of the antibiotics that his particular Pseudomonas is sensitive and resistant to? I have read about using Tris EDTA nose drops, along with nose drops of the appropriate antibiotic. The Tris EDTA helps break down the "biofilm" in the nose protecting the bacteria, so the antibiotic can get to it.
Using Gentacin eye drops, as nose drops, has helped some cats with Pseudomonas nasal infections.
Using Zithromax for months helps some of these cats.
More research: amitriptyline (an antihistamine and anti anxiety medication) helps with chronic nasal infections; like the Tris EDTA and eye drops, it helps the antibiotics to work better and get to the bacteria better.
Let me know what other questions you have about HIM (so sorry). Rebecca