It seems like the music actually changes depending on the situation. For example, the first piece that's played on your second upload can take an entirely different approach. It's almost like you have to edit a whole sequence just to get it all in.
That's actually not uncommon for MIDI music in games. That's actually the reason why in many Windows games, you'll often find it in XMI as XMI is a much more simple format than the regular MIDI format to loop and give commands to switch to another.
If one could crack the code and the format of Judgment Rites, you would get all different pieces as separate files and even one piece splitted into two. And then there's of course alternate versions.
But since I have not been able to establish anything else beyond that it seems Judgment Rites uses the XMI format, more common for later Windows games, I cannot verify my assumptions. All of the music in my videos are recorded during gameplay. For Judgment Rites, I actually mostly used DosBox's own MIDI recording utility but I do tend to use different MIDI loopback drivers also.