Sorry, I’m only here sporadically unless a direct reply triggers an email.
Given the asymmetry between your ears and the amount of damage to the left ear it’s not that surprising to me that you’d be hearing pitch differently in both ears. The hearing aids can’t compensate for it, unfortunately, and it wouldn’t generally be a linear shift anyway (e.g. you couldn’t just shift all tones up one semi-tone in the left ear and have them match the right). Just out of curiosity, how far off are your two ears? How far off are they for low tones versus high tones?
If you’re trying to improve you music program on your hearing aids, I’d recommend asking your practitioner to mute the left ear and adjust for the right (leaving the two linked). Pull up a song on youtube that you are familiar with and which sounds “off” to you and play around until it sounds better–you may want more highs and lows that a typical speech-focussed program, and your own voice might wind up sounding odd but that’s okay so long as you aren’t singing.** Then unmute the left hearing aid and if it is distorting things drop the volume down until it sounds better, leaving your right ear dominant for music-listening.
Also, how long has this been going on? I’m put in mind of something I heard or read recently about a patient who got a short-array CI in one ear and then a few years later got a full array in the other ear. After training/adaptation they ended up pitch-matching across ears even though the two CIs were stimulating completely different areas of the cochlea (given the different lengths of the arrays). The brain adapts. I wonder whether one could train diplacusis away somehow. I don’t know what the input would need to be, but I do know that the beneficial auditory processing effects of music are only available to people who play music (vocal counts), not to those who just listen. You need to be actively working at it. Perhaps you should take up a new instrument.
Alternatively, it might be a good time to explore different types of music. Harmonies may not work so well for you anymore, but there’s some neat rythmic stuff out there. (Also, if you are attending live concerts you might want to slap a couple of layers of scotch tape over your hearing aid microphones to reduce the input and avoid distortion that is happening there, too.)
**(Wait, you ARE a singer. You’d need second music program for when you yourself are singing).