That "start playing an instrument" advice is total bullcrap. Starting to be a musician wont affect how well you can hear and in many cases you will find that musicians have awful hearing; both in a literal and then an aesthetic sense (they cant tell what "sounds good" from purely a sound perspective).
You could take estrogen, but I would advise against it.
Hearing loss is not permanent, there are permanent forms of hearing loss and those considered "permanent" because they take >40 years to recover. The best process to improving your hearing is to turn down your music (lower and lower and lower); your ears will be able to recover from recent damage they have received (sometimes it may take up to two years, and you will probably never get to hearing as good as it used to be) but more importantly you will become better at using your ears. Ever wonder why there is the stereotype of blind guys with fantastic hearing? They have to rely more heavily on sound than we do; they consciously use their ears to hear "sound". So do audiophiles. Musicians simply hear music.
Hearing the difference between headphones beyond EQ has nothing to do with musicianship; I have been a practising musician for most of my life and if anything it hinders your perception of detail in audio. If you improve your musical ear you can hear what happens in music, the tones players use and also the chord progressions and what is being played. It WONT let you hear the difference between DAC A and DAC B. The only way to hear the difference between DAC a and DAC b is to listen to music and be aware of the microdetail in the music.
There are many people who believe that being a musician hinders your ability to discern difference in music with regards to sound quality because you focus more on the music and what is happening within the music than within the sound.
All of this said, being a musician is one of the most difficult and most rewarding things in life. If you have the time and patience (you dont need talent) I suggest you to learn. Dont just try and learn the instrument; try and learn music. The sounds, the musicianship and the ear (hearing what is hapening in music, for example hearing a I vi ii V I progression). Being a musician may very well be a way to improve your ability to discern difference in equipment; I find it very easy to tell the difference but developing your ear musically is very challenging. I have spent a lot of time with audio equipment and I have been listening quietly for a long time - I know how to listen to the sound as well as the music after many years of practise and i know what to listen for.
It just takes practise. Listening quietly is one of the most powerful steps you can take in training your ears to hear "audiophile sounds". The ears are amazing things, even when damaged. They speak to you every day, you just have to listen.
