Okay so update to let you know that I think you're on the right track. Since you mentioned those folders, I tried removing the "playlist", "platform", and "platform categories" folders from the background music folder entirely. The result is that now when Big Box loads, after the initial random song plays, it shuffles to another random song. BUT... after that it continues alphabetically after the 2nd random song. Example song order: "Mega Man 2 Theme">"Click Clock Wood">"Clock Town Theme">"Cloud Cuckoo Land">etc.
Once I enter games lists from the platform list, Launchbox makes the "platform" folder again in the background music, and it shuffles back to the first song alphabetically (as in something starting with A).
Hope this helps to unravel the mystery a bit more.