Preliminary testing on the current population suggests that a one-level drop is not enough. A setup like the following will provide a two-level drop:
z+0
#####
##@##
##+##
#...#
#.<.#
#...#
#####
z-1
#####
#####
#####
#...#
#.#.#
#...#
#####
z-2
#####
#####
#####
#,,,#
#,#,#
#,,,#
#####
1. None of the access is shown here. You'll need a down stair on z+1 to get into the drop chamber, and some way of getting dwarves from z-2 to either z+0 or the hospital.
2. The door (as represented by the +) is set to Internal, and the barracks have to be sized from the barracks furniture (@) while there's a path between the furniture and the up stair. A floor constructed after all the digging will be fine.
3. Masterwork leather is not sufficient to prevent this drop from jamming a dwarf's ribs into their heart. Any sort of metal mail shirt and helm should be mostly fine, although I wouldn't rule out lethal injuries from copper or bronze, or even anything else. The RNG can be a little extreme.
4. You can make a one-level drop and, after removing the ramps, fill the eight tiles with six lots of 6/7 water and two lots of 7/7 water. The 7/7 tiles allow the dwarf to climb out of the water once they reach Novice Swimmer, and the 6/7 tiles prevent drowning and hold the dwarf in the pool long enough to gain a significant amount of XP per drop. Injuries are something of a concern in this setup, though based on some DFHacking on an unconnected dwarf* even dwarves who can't walk will drag themselves out of water. Dwarves who would normally wait for recovery may also move if a civilian alert is activated, and I did this on a couple of occasions where masons were getting shot at by the magma crab.
*Got taken to the hospital, starting getting ignored at some point and started to dehydrate and starve. Study of the situation resulted in the titbit of information here, and in the end I retriggered a recovery job by dumping logs on her until she was sufficiently injured for medical care. Again.
Edit: I expect this would be a pretty good way of boosting Armour User skill while still using the regular military system, at least for dwarves who don't have the equipment to block or parry the ground. ...Can they even do that? I'm just going to assume they can, because that's the option that makes the most sense.