I have no idea why, but installing the newer version of TiMidity has solved the issue with the sound, which I hear. The complete timing of the sound seems now corrected. There is no false volume ramping anymore. It doesn't repair some background sounds, which disappear when another sound is playing, but most of them can be fixed with some changes in the script.
You don't need to play the music with Midi, you can still use FF7 Music.