Apple Music 1.0.6.10 BUG: playback stutters with LOCAL files

None of that is applicable. As noted originally, I suspect there is a bug in the Apple Music application's buffer management logic. This wouldn't be the first time. For years there were problems with iTunes/Music's buffer management as it interacts with the Sound Check feature. When playing a series of songs, the first 8 seconds of the next song would play at the Sound Check level of the previous song (i.e. the volume leveling was being applied when loading the buffer based on the currently playing song's Sound Check level, rather than when reading from the buffer using the applicable song's Sound Check level). To this day, this still results in some songs starting off louder or quieter than they should be on some older devices, then adjusting 8 seconds into playback.