Just go into your memory/music manager in the dash and make a custom BO3 playlist by copying all of the songs you want into the new playlist. That way, you'll get all of the songs you want to hear during play. EA/Criterion's implementation of CS is poor, IMO.
Select Driver Details from the Main Menu
Select Settings
Select EA GAMES TRAX
Now here simply press the X button to select what Music compilation (the one you created within the Dashboard) to play in the game.
Unfortunately the game doesn't save this setting so you'll have to do it everytime you want to boot up.