I might have stumbled on a clue towards applying Adapt Sound globally or with different music apps.. I was fiddling around with it the other day, and then I was testing the Samsung music app and Google Play Music. Of course, music played through Play Music did not enable the Adapt Sound.
However, when I was listening to a song in Play Music, I thought I'd open the Samsung music app to try to run a comparison, and as soon as I opened it, it applied the Adapt Sound to the music that was playing through Play Music! It seems that when the Samsung music app opens, it enables the Adapt Sound regardless if it's actually playing anything or not, and simply keeping it open in a second window (I'm on a Galaxy Note 3) kept the Adapt Sound enabled! As soon as I closed the Samsung music app, the Adapt Sound was disabled and the sound reverted to the default. Perhaps this may give a clue on how Adapt Sound is applied through the Samsung music app, and perhaps make it possible to make a widget with a button that can enable or disable the Adapt Sound feature.