So, I ended up using a modified version of the GCS silk farm on the wiki. I set it up so that the spider would shoot at a bait goblin, webbing the cage traps behind it. There are two paths to the fort from the spawn area. The one on the left is an access tunnel that is always walled off except when it's time to grab a cage and reload a trap. The other is open most of the time to lure in FBs, but dwarfs are blocked by locked doors to keep them from wandering in and getting caged/killed.
Unlike the silk farm on the wiki, I made the fortifications only 1 tile wide since I'm only webbing traps in a straight line. I also added a door at the south (rear) that you can unlock to let the spider out if you need to move her to safety or to another webbing setup.
It's working pretty well so far. I've caged all six FBs that have wandered in. I had a bit of trouble luring the last one in, but eventually coaxed it into a trap by dropping bait (goblins) in from above. I occasionally cage a dwarf or two, but sometimes caging and extraction go smoothly.
On a side note, all six of my FBs have spawned from the same spot. It's also the only spot where the ground level of the cavern is not walled off. Even though regular critters can (well, they used to before they stopped spawning) spawn on top of walls blocking the cave entrance to enter at a higher level, it seems that FB's either must spawn at ground level openings or prefer to do so if they can.
Also, I still haven't managed to coax any cave critters to spawn (other than the occasional gremlin) since depleting the caverns one by one. Does anyone know if I can get this going again? I'm not sure if caverns keep track of a wildlife population like above-ground creatures do, since it seems odd that you exhaust each cavern independently, one at a time.