The short answer is speak to an audiologist who happens to be a musician or audiophile.
I am a doctor with a background in neurology and things perceptual including neuropsycholgy and rehabilitation but I am not an audiologist or Ear specialist. The roll off of 20Db per octave sounds steep, yes.Hower 2 things in your favor are you have only one octave (2500 - 5000 Hz) of impaired hearing response falling in what most people would say is mostly required for musical appreciation.Secondly,one hearing impaired musician told me he places more imortance on the lower frequencies for musical appreciation, (and higher frequencies for speech,sibilance etc).
The upper range of a piano is a bit over 4kHz (4000) and between say 40 to 4000 Hz lies the bulk of our musical experience. One octave above this upper limit is 8kHz (2 x 4) and 2 octaves is 16kHz (2 x eight). Sounds above 4kHz or 5kHz progressively tend to be 'amusical' lacking 'timbre' or character and a large part of this is because their harmonic overtones become inaudible (for practical purposes lets say above 16kHz).These sounds may in fact be unpleasant to hear and in some cases may be felt rather than heard.
So getting a digital hearing aid if rquired can be, I am told by musicians, very helpful for some.If the hearing loss is not too bad many prefer not using a HA. The problem is everyday HA's are optimised for speech loudness levels etc.They distort with higher levels typically in music.I know you can get HA that are 2 channels, one for speech and other set up for music!Either way it will depend on whether you have a flat loss or specific loss, the HA adjusted with things like EQ,compressors-expanders,limiters etc.
I cant talk about the DSP in MC as I do not use it ( a purist audiophile,lol).Howver, if you went down this route then you would be the only one able to listen to your 'colored' music (unless your fellow listeners enjoy the coloration).Part of the fun in music is sharing.What about live music etc
All the above has been on more or less biological and physics.You should also be aware of the strong role of conditioning, learning and training (aka listening skills) we know to be involved in all sensory perception. This works in your favor also.We all know that music and sound is an interpretation that is made in the brain based on a chain of events commencing with the physical stimulus. We also all know music can be enjoyable even in a truncated narrow frequency range but can you hear stuff thats not there..., huh?! I believe the physical measurement is only one part of the perceptual equation. It is likely people learn to perceive frequencies that they cant literally hear.... A bit like Beethoven composing music when deaf. If you hear the lower harmonics of a note it is not outrageous to consider the possibility that the brain extrapolates to "hear" what it thinks it should. After all you dont need to have a left foot to feel a left foot....maybe you have heard of phantom pain? With music it may well be that this works only with familiar music ie where the brain has a strong memory of the sound/music. This has to do with pattern recognition and the the brain attributing meaningful interpretations.I knew a near deaf cardiologist that could 'hear' heart murmurs better than the young interns ! he could detect the faintest murmur but was 'hard of hearing'.