I have just posted Xump for PS2 v1.06.1, a major bugfix release over the previous version. All known bugs with the PS2 port have now been fixed. This includes the issues with the music and menus, and it should now boot and run correctly on the very early Japanese PS2s.
A big thanks goes to Evilo. It's no secret that I have not been enjoying working with SDL, so my good friend Evilo volunteered and stepped up to get Xump working with sdl_mixer. Thanks Evilo!