So do I
As most people here know I was born with right sided SSD +120db, and almost normal hearing on my left. I had frequent ear infections which then lead to permanent mild/mod loss (fluctuating) on my left - I also (interestingly enough) have APD.
The really ODD thing, is that I have a nearly eidetic memory for music - by which I mean that if I hear AND feel (vibrations) a piece of music I almost always am able to "play it back" in my head and have it sound identical to how I originally heard/felt it - like a CD playing in my head.
Regarding the OP's post - I can completely relate as I've played musical instruments since I was about 6 (piano, violin, flute, sax, clarinet, piccolo, trumpet, Bassoon etc). I actaully played in a semi professional orchestra for a number of years (I played flute and Piccolo - mainly Picc, the upper freqs I actaully hear reasonably well) and played a concert with the professional symphony orchestra in my city when I was only 17years old (playing flute & piccolo for the Saint-Saëns organ symphony). I typically practice in bare/socked feet while facing either a flat wall, or a corner (depending on what I'm practising rehearsing) so that the sounds & vibrations reflect back to me... I also rehearsed (ie orchestra/group ensemble practices) in bare feet/socks (so I can "hear" better via the vibrations) and either short sleeves, or long sleeves of a light weight material to optimize the vibrations in the air - actually, in Orchestra concerts (since Flutes & piccolo sit mid orchestra behind the violin section and our feet aren't really visible) I'd often subtly slip off my shoes during a concert and tuck them under my chair so that I could hear& feel the other instruments well.