I've been thinking off and on about a similar idea, but not quite as extreme. My concept is that starting seven are religious outcasts, who believe that the surface and everything there is evil, and that the only way toward eventual salvation is to flee the mountainhome and build a new society that doesn't even know the surface *exists*.
So, no trade, no surface plants or wood, and everything designed around making as much of society as possible revolve around underground resources that are infinite, renewable, or are at least infinitely recyclable. I was also trying to avoid use of exploits like remelt amplification and quantum dumping.
With the right site, you can have infinite water, magma, sand, and clay. By combination you also get infinite obsidian (stone) and glass, which can also be cut into gems. A properly constructed underground farming complex can generate renewable food, booze, cloth, and wood indefinitely. Optionally, carefully chosen animals can provide meat, eggs, leather, bone, and shell; and the farms can produce dyes. More elaborate systems may be capable of producing spider silk, but I'm uncertain whether this is truly renewable; once the spiders start dying of old age, are they replenished at a sufficient rate? Getting an ageless FB (or demon...) that generates silk may be a significant long-term investment.
As you eventually uncover all the available caverns and finish digging the fortress, the strange moods will taper off. A side effect few consider is that Legendary crafters will be in much shorter supply once past the first generation or few; in combination with the increasing scarcity of metals, this will naturally result in a situation where the weapons and armor produced in the early days will be dramatically better than the every-day ones of later generations.
Looking forward, leather and/or bone armor and obsidian swords will likely be the default equipment for the military; perhaps a somewhat Aztec-like style might emerge. The masterwork metal items of yore will be carefully treasured relics, far better than the mundane gear but brought out only in case of extreme need; if lost in combat, they cannot be replaced. Few if any areas will not be under control of the fortress; lakes whether of water or magma will need drain and refill options to recover valuable items, for instance.
The slab issue, which I had not considered in detail, will eventually doom such a fort however. It might take thousands of years, but eventually, the fort will mostly a necropolis, full of memorial slabs everywhere they can possibly be placed. Unlikely combinations of failures will have damaged the various networks or regenerative systems (e.g. all of a generation of animals are non-breeders, series of unlikely farming failures and bad timing destroy the last seeds of some plant, etc.); the animal systems are the most likely to go.
Eventually, you have a gloomy fortress subsisting on plump helmets and clothed in coarse pig tail cloth, with large areas sealed off due to fluid errors or unkillable FBs. Of course, then one day a rebellious young dwarf will flee the oppressive society into a sealed tunnel, find that the FBs trapped beyond generations ago had killed each other off, recover a wondrous set of steel armor and a sword from the corpse of his great-great-grandfather who died fending them off long enough to seal the tunnel, plus a mysterious magic item long forgotten except in old children's tales, the "pick" - it lets the user *go through walls*, and can even carve new staircases up! Drunk with the power, and yet knowing that the fate of his fortress depends on finding new places for slabs, he digs up, and discovers a strange world of dangers, wonder, and possibility, the "surface".
Perhaps this is how we get our first YA novel inspired by DF (and innumerable pseudo-SF stories from the '60s and '70s)
Or, perhaps, a darker tale; the slab crisis has progressed even further. Dead dwarves are not slabbed unless they turn out to be exceptionally dangerous; the forlorn haunts far outnumber the living. All automated systems are long defunct due to poltergeists messing with levers and misplacing mechanisms, and huge areas are unlivable due to fluid systems gone awry with no remaining means of repair. Our brooding protagonist flees as before, but after grabbing the gear digs up and encounters the legendary Seventh Founder, sealed away for a crime so unspeakable that it's no longer known... and still alive, or some semblance of such, a slow moving, mad vampire in a hermetic tomb. After accidentally tasting the Blood of the Founder in the process of killing it with his shiny steel sword, he realizes in a desperate incident (perhaps digging up into an aquifer) that he no longer needs to breathe or eat, will not die, and that the only long-term salvation for his fortress lies in him bringing the Blood of the Founder to all dwarves, whether they are willing or not. After devastating the old power structure in one, final, round of bloodshed with his dark strength and bright sword, converting those he could and slaughtering those he could not before they bred another, disastrous round of ghosts, he rules the new fortress. And, eventually, as the seasons and years pass, realizes that he hungers, *always*; that there is no new *anything*, including dwarves; and the fort fades into the darkness of eternity, ruled by an angst-ridden teen brooding on a throne of blood.