I suffer from pitch distortion. I am not sure if it is divergence between my two ears, or divergence between different instruments (i.e., different overtone spectra) and/or octaves.
For me, string instruments are the worst, often sounding grossly out of tune. Even when things don't sound out of tune, with works that I know, since I have had perfect pitch all my life, what I hear sounds as if it is in the wrong key, which is quite jarring.
Ear-Nose-and-Throat docs and even audiologists who I have asked about this pretty much just shrug their shoulders. My guess as to why it is happening is that, with degraded response from the auditory hair cells, the cell pattern that responds to a given pitch (say, A) is different from the cell pattern that used to respond to it (prior to hearing loss) and that is mapped in the brain to a different pitch (say, B-flat).
As a composer of contemporary classical music, this seriously complicates my work. I worry that what I am hearing is not what another listener will hear. I employ a few imperfect, pragmatic methods to mitigate this risk: I use midi-playback with "instruments" that I hear with less pitch distortion (even if they are not the instruments I am composing for); I play the music back with and without hearing aids, and with and without headphones, since I have noticed that distance also plays a role (perhaps a Doppler effect).
But it is frustrating and, often, depressing. I do believe there could be technological solutions to this (I also work in IT) but they would be very specialized and might not be easily marketable.