To block music such as these, you need to change the way you do the triggers. This is the bast way I know to overcome the problem.
(a)Use play diologe to play the music instead of using it to show those messages in the black bars.
(b)Use sound filename to add the words on the black bars at the bottom and for any adittional sound effects e.g. an evil laugh
If you use play diologe for music, when the cimatic starts, insert a trigger called play diologeand leave the sound on default and it will BLOCK the music that is currently playing, even if it is not the main age of mythology music.
If you want any music to play in the final cimatic then change the sond called default to the one you want.
This trick works on the fact that only one diologe can play at a time so it means that if you use play diologe to play music, on one set of music will play at any time!
I am a little confusing but if you try it, you may understand what I mean.