This UberASM will make each OW submap have a different song when a certain event has been passed (it only works properly if using AddmusicK). Make sure to check out the included readme file for instructions on how to use it.
I noticed that the music doesn't change properly between worlds when you enter a map through an exit tile rather than a pipe/star until you exit a level (the game runs the music of the previous map even setting everything as your Readme stated and assuming the last event didn't trigger the music swap when activated), so I had to reset the music via Lunar Magic to its original values. However, the music changes correctly when the event triggers the code (the music here is set to be 00 as intended and you warp here via star).
I'd like to add a small note to what the readme says: the issue where using the same song in an OW map and in a level accessible from that OW map is not actually caused by this, but it's a problem with AddmusicK. In the end, the consequence is the same: don't do that if you don't want the level music to fade out instantly.