Didn't they say they were going to implement a toggle so you could deactivate the battle music and just play the dungeon theme throughout? That said, while it's not a perfect solution you do always have the option to mute XIV's BGM and supply your own. Sometimes I even load up a TeamFourStar video if I'm in a dungeon I don't particularly like, to take the edge off. (AK, I'm lookin' at you. >>)

As regards your other question, basically roulette assigns you not to a random dungeon, but rather to a random DF party within that set of dungeons. So if most people are queueing for, say, Pharos Sirius, you'll be more likely to get that.