Before you turn to a factory reset, since you are balking at the idea, it seems there are still alot of variables you could consider.
Have you uninstalled or disabled ANY stock software that comes on the phone? Sometimes applications have been tied together, and inhibiting one that seems unrelated can have negative results on other applications. For example 'Car' or 'Soundhound' or 'Tune In' all have ties into the music application and eachother. There could be other programs with ties in that are much less obvious than music related.
If you have any kind of task manager/power managers installed it could be halting the audio enhancer without your knowledge.
In your photo Power Saver was on, maybe it halted the Music Enhancer to conserve CPU cycles?
Music also has a settings for automatically updating Album art, Artist Photos, and Lyrics. If the phone is trying to update these in the background and it cannot connect or is running into issues I could easily see it crashing music.
Then there is also the question of what media you are playing. Are you playing music stored to the internal Multi-Media Card (storage)? Is the player crashing on a certain filetype? Or is there a pattern with it crashing on the same song repeatedly? If you've got media that is even slightly corrupted or has a filetype that is not supported, it could crash Music.
If you are streaming from a server over IP, that opens a whole bunch of other variables that would to be easy to troubleshoot. Localized media would be easier to investigate and probably more reliable than songs streaming from Dropbox, Amazon, Google servers, or other.
Stock, the Music application (with headphone icon) should have 20.00KB total data attributed to it. Music Enhancer (same headphone icon) should have 52.00KB data attributed to it. Both can be cleared to 0.00KB and restarting Music should automatically set them both back to 20KB and 52KB