Just brainstorming out loud, but I wonder if perfect pitch could be improved by regularly playing each of the 12 pitches with a different timbre. The brain might become used to associating a pitch with something that the brain can latch onto more easily (timbre). 
Example: I don’t know off the top of my head what a G♯ sounds like, but I know what a clarinet sounds like. The clarinet’s tone quality would be the “mnemonic image”.
I don’t know if it would work, but I’m thinking of something similar to how relative intervals can be trained by relating them to parts of songs — example: major 7th is the interval between the 1st and 3rd notes of Somewhere Over the Rainbow. If you want to find the M7 interval without an instrument, you can sing just those two notes of the song. Timbre would be a little different, but it might be worth trying.
Here’s a related article I saw this morning:
They found that in both groups, the FFR—which provides a snapshot of the integrity of a person’s ability to process sounds—predicted people’s performance on pitch identification better than any metric previously used in studies of perfect pitch, including musical training.
Participants also tended to be better at naming notes played on a piano as compared to the computer-generated sine tones: Those with perfect pitch averaged 98% accuracy on piano and 77% for sine tones, while those without averaged 29% accuracy on piano and 25% for sine tones.
According to UChicago doctoral student John Veillette, who was also a co-author on the paper, this suggests that timbres—which are conferred by upper harmonics in sound frequencies and give instruments their unique, familiar rings—play an important role in pitch recognition.
Reis said that implies that experience is probably involved in pitch recognition, since even people with self-reported perfect pitch weren’t “perfect” when the notes were produced in an unfamiliar way.