The problem isn't whether you "have time" to learn music. Of course you do. I taught myself to play the piano at the age of 30. (With a solid background already on another keyboard instrument, the venerable accordion. Lawrence Welk and Myron Florn were big for my parents when I was growing up....) The problem is that it may be yet another of those things that you learn well enough to do competently, then get bored with it. As I did with the piano. (My level of "competence" might not be as high as most of yours in this particular field. I got to the point where I could not only play several songs from memory, but could improvise confidently within those songs. I've been away from it long enough now where going back to it and studying piano/music again might be fun, besides which the only song my fingers seem to remember at this point is "Sh-boom." Not exactly a dazzling repertoire.)
Honest, I really think a quest to find one perfect source of permanent fulfillment for any INTP is about up there with finding the Holy Grail. And this is one of those deals where thinking about it won't clear it up, you'll have to experience it. (Which I've done, you'll notice, but you'll all have less faith in my own experience than you do in your own. :-) )
I am ready to stand corrected and be cheerful and gracious in the process, but everything points toward a series of professional/vocational/personal interests over a long period of time. And if you find me an INTP who has been happy in one profession for, oh, 35 or 40 years, I'd say look at the particulars of that profession and you'll probably find that it in itself has changed over that period of time.
Just sayin'. I regret, for the one thousandth time, that I never knew all this about myself at the age of 14. It would have saved a lot of turmoil. :-)
Thats a productive life, you seem to have overcomed some of the INTPs flaws. Kind of makes me wanna quit my meaningless job 
