I think you're right as far as the cause of the bug being the leaving of the area before a song finishes. I can vaguely recall leaving mid song and realizing I had broken something but my save was considerably far back progress-wise so I ignored it.
Good to hear that the Xbox version should be up to date. That eliminates any possibility of the bug being caused by an out of date version.
It'll take a while (I was a teen when I first played the game, so I had more time to dedicate to it), but when I reach that point in the game I'll be careful not to interrupt the song playback. I'll see if I can reach the end of the game without the bug occurring and I will update this post to help anyone that tries to find information about this in the future.
