Great. So you have both playlists, right? Playlist "Alpha" containing songs 1-5, and playlist "Beta" containing songs 1-5 and song A. Both random step, as you pointed out.
Now, on the Game Syncs tab, under Switches, you should create a new Switch Group; let's call it "Level Stage". Within this switch group, create two switches: "Initial" and "Quest A completed" (I'm sure you will come up with better names depending on the whole level possibilities, and you could add all the extra switches you may need).
For these to work, you need to link them to the event you mentioned ("Quest A success"). Select that event from the Project Explorer, in the Event Editor, right-click and create a New Action > Set Switch; then right-click on the red box and Set Target > Quest A completed (you can also drag and drop the switch into the Event Editor view). Now when that event is triggered, the switch group will change from "initial" to "Quest A completed". You should make sure you set this group to "Initial" when the level starts using the corresponding event (it's the same process, but you add the action Set Switch "Initial" to the "Start Level X" event).
Now, back to our Project Explorer/Audio tab. You should create a new Music Switch Container, which will call "Level X Music", or whatever. Move both playlists, Alpha and Beta, inside Level X Music. From the Interactive Music layout, select Level X Music and link it to our Switch Group: "Level Stage". Drag playlist Alpha on top of "Initial" and Beta on top of "Quest A completed".
You can test it using the SoundCaster. Make sure to go to the Transitions tab within Level X Music, and define your transition rules.
If I was unclear, let me know and I'll try to add some images.
Good luck!