Here is how I'd do it
Legend:
O = wall
. = empty space
X = floodgate/door/raising bridge
c = cage
O O O O O
O O c O O
O O . O O
O O . O O
O O X O O
O . . . O
O . . . O
O . . . O
O O O O O
So you prepare a 3x3 room, and have a short tunnel leading to it. The tunnel is disconnected from the fort after the cage is set up, and the cage is connected to Lever 1. The X designates a floodgate or a door, something that breaks line of sight. Connect that to lever 2.
Seal the entire contraption away from the fort, and pull Lever 1, releasing our dear friend. He or she will then wander the area, eventually reaching the 3x3 room. When that happens, pull Lever 2 sealing them in. Now I'm not sure whether zombies can break doors/floodgates so the next part has to happen quickly. You would take down the isolation wall, and build a new one farther in, just beyond the cage. When that is done, the cage is accessible and the zombie is completely sealed within constructed walls.
An improvement on the above would be an empty tile (NOT A RAMP) below the X, and X being a raising bridge. That way, once it retracts, it blocks line of sight to the zombie and prevents movement. It can be lowered once the area is sealed.
A more complicated, but even safer way (because I don't know whether zombies break floodgates/doors) would be using a cave-in. In this case, you would set up a larger room, say 5x5, and a smaller room above it, say 3x3.
Legend:
O = wall
. = floor
_ = empty space
c = cage
# = horizontal bars
* = support
Z=0
O O O O O O O
O . . . . . O
O . . . . . O
O . . * . . O
O . . . . . O
O . . . . . O
O O O O O O O
Z=1
O O O O O O O
O _ _ _ _ _ O
O O O _ . . . _ O
O c . # . . . _ O
O O O _ . . . _ O
O _ _ _ _ _ O
O O O O O O O
So empty the cage, collapse the support, and the zombie tumbles down. I don't think we care whether they get injured, or even die. Then the cage can be safely retrieved and recycled.
Alternatively, replace the # with a retracting bridge that retracts away from the room. This would create a LOS seal.
FINALLY! You could set up a contraption where the zombies are stockpiled in cages in an isolated room with a minecart just below. Pit the zombies to be dropped INTO the minecart, and then deliver it to drop off ABOVE their designated room. This would be complex and slightly risky to set up, but would allow the system to be reused with only minor modifications to minecart tracks.
So, Z+2 = zombie stockpile with a hole in the floor which is a pit
Z+1 = minecart receptacle and minecart tracks leading to a hole above destination room
Z=0 is where the room is located
I, however, don't know how to set it up. I just know HOW it works.
I have more ideas. I may post them later.