I couldn't reach any cave, I have encounters while exploring the surface and since it crash after the encounter I can't finish exploring. Maybe if I try enough I can have an exploring run without encounters and be able to try the caves 🤔 got nothing better to do rn, I'll give it a shot.
EDIT 1
So I gave it a shot and managed to reach the caves. Same problem. Crash after a battle.
I dis another test, saving on the surface and in the caves. The crash appears too when loading those saves. I guess it's related to maps initialization, something between load/initialize functions and around the loading of 
So to summarize. Going on the surface or going in the caves works. Crash happen when loading on those areas or after a battle in them. Sometimes, because of the freezes, the above can't load properly. Sometimes the "Retry" buttons works, if there's not too much freezes, but it still crash. To me, all of this indicates a loading/initialization process bottleneck on maps, the fail to load of the bgm is probably a symptom of it. One solution could be to fully preload all audio at game launch, to free some processing at maps loading, or try to find tricks to load things separately instead of all at once.
I'm gonna fiddle with Joiplay options now.
EDIT 2
I can confirm changing everything in Joiplay's settings doesn't change anything, neither does using the Game.exe or the index.html.
EDIT 3
I fiddled with plugins, and nothing changes for the crash. That said, disabling ShoraLightning greatly improves FPS in the cave (as expected) but obviously removes the dark tone and torchlight. You might want to look for another and maybe better optimized plugin for that, or use parallax mapping for the dark tone.
I don't think I can help more in the current situation unfortunately :/