OP: Turn it sideways.
Instead of a central staircase, make a central hallway, with rooms branching off upward, downward, and sideways! Put the entrance on one side, of course. When you hit the end of the map, go down enough z levels for rooms, and go back. Zigzag down.
I've lately been trying to build a five-part fortress design, to some success, built around a central staircase, though. Basically, I try to have 5 different mostly independent forts- Surface, Cave 1, 2, 3, and Magma. Each has its own focus. Surface does farming and woodworking, Cave 1 does animal stuff. Cave 2 does mid-value natural products crafting-cloth and silk type stuff. Cave 3 does combat, has the main tavern, has the main library, is generally the center of attention. Finally, Magma level has the high value crafting, weaponsmithing, magma forges, as well as the catacombs, the artifact storages/displays, the statue room full of epic fortress-relevant (though, somehow, inexplicably, always the crappy ones) statues, the noble's quarters, and the rooms of the worthy dwarves, whose ranks are populated by the best weaponsmith and the best armorsmith in the fortress, anyone else that's got legendary skills outside the craftsdwarf's shop, and the occasional war hero that is too maimed for effective combat but is still somehow alive. The idea is to devise a caste system among my dwarves, where their ranks are dependent on the level at which they live. The more worthy ranks, of course, living closer to the blood of the mountain.
So far I have done this in two ways, the first of which is mostly independent forts with burrows, which really loses the benefits of the focused industries, and really seems like the hermit challenge from the wiki, but with a delayed separation. The other way is to have each fort intentionally focus on a few industries exclusively, and rely on a sixth caste of "untouchables", or hauler dwarves that earn their meager scraps to eat by delivering goods between the proper forts. They, of course, sleep in roughly carved out communal barracks near their work sites. Either way is incredibly time consuming to set up and is likely to result in a few injuries. My advice is that each level will need its own local squad, and it's best to set those up first.