I like this idea, very much, and I'll second the idea of a band/choir (Dwarf opera for the win).
Some of them might be private about it, but music and bands have always been a good way to entertain everyone, and even to record historical moments.
Songs could maybe be a little like engravings? "Urist McDrum sings a song about a dwarf surrounded by goblins. The goblins are taunting the dwarf. This relates to the seige of so and so, that occurred in the year whatever."
Also, if there's bands, they could be organized in the same fashion that we organize military squads, with different bandmembers assigned different instruments.
They could get their own randomly generated name, and be assigned to play in certain areas. Not all the time though. Maybe they'd just gather once a week for an hour or something.
And to further the link between bands and squads, maybe sometimes a squad that's been in existence for a while could just up and decide to become a band on their days off. If nothing else, it would improve cameraderie, morale, and their ability to function as a unit.
I've also thought that it would be awesome if it were possible to build a Fortress around an immense, skyscraper-sized, magma-powered, pipe organ, built into/out of a mountain, with the deepest pipes going down through all the Z levels. Classical organ music seems fairly "dwarfy" to me, especially in combination with the idea of an insane Philosopher Noble playing it in the middle of a busy fortress.