To gain experience? To learn the challenges & pitfalls of the field on someone else's dime? To learn from somebody who has been doing it and getting paid?

Nobody jumps from the bottom of the mountain to the top - you climb it one step at a time. There are people making a living producing music and writing apps - the world does work that way. I'm not saying tomorrow you can decide that's how you'll make a living and it'll happen - but it is something you can work towards and achieve in a reasonable amount of time.

To get better, learn how to run a business based on building such software so that you eventually have the resources to pursue your own dream.

Why would you not want to do that instead of a job which you admittedly feel rather "blah" about?

Presumably because you can't afford to pay rent doing it for your own.