I think part of the problem with that is that you're trying to literally make it a game for everyone, which just won't happen. This game is already so many different things for so many different people that it's fairly unweildy to keep the playerbase together as it is. (Look at the arguments between whether the game should go towards steampunk or magical dwarves. Or graphics vs. ascii. Or bearded females vs. non-bearded females.)
The adventurer mode and the fortress mode are pretty separate entities which draw separate people to play it, and adventurer is only finally getting some much-needed attention recently. (And I still won't play it until there's more to do besides killing things.)
In order to make the game a great game for a decent-sized chunk of the population, you have to stick to some sort of formula that really will bring people in, and make that portion be the best it can be. If you try to make a game a Street Fighter/Final Fantasy/X-Wing Vs. Tie Fighter/X-Com/Thief/Halo all at the same time, you're never going to be able to do anything well for trying to do everything at once.
Now, to get back to why "directed goals" are a bad idea... Trophy/Achievement unlocks are things which just encourage players to do things they don't like simply for the measely reward of an icon being put in color in a menu that only they will ever care about. Almost nobody actually goes for the platinum trophy, because nobody will stick with a game long enough to get it. They want to play the game long enough to have fun, then move on when they're sick of it.
If the only way you can think of to entice a player to play Dwarf Fortress is to give him a sticker for playing, then he's probably not going to enjoy Dwarf Fortress very much, since it will just be a chore standing between him and what he really wants, a sticker, not having fun playing a game.
If you want to have "directed goals", then perhaps you should be trying to think about ways to create alternate game modes, or have some sort of directed goal that could be put into the game itself that wouldn't impair the sandbox lover's fun. Toady is already talking about making fortresses that have specific missions directing them from the start. That's a directed goal that is rolled up in gameplay.
Alternately, you could try getting in some tutorial mode, since that would make this whole argument I've been making go along one continuous, cohesive narrative, and setting clearing some set, arbitrary tasks that incrimentally teach the player certain skills necessary for building and maintaining a fortress.
Beyond that, really, fuck 'em. You can't ask a game about simulating aerial dogfights to have a turn-based mode so that it appeals to a broader audience because not everyone likes airplanes. You play a game about dogfighting in airplanes because you like simulated airplane dogfights. If you don't like airplanes, then you just walk past that game in the aisle, and there's really no problem with that. There's enough games out in the market that DF doesn't have to be every game at once.