create small corridor full of spikes linked to a trigger, put the lever on repeat and open the cave. Spikes are extremely lethal to FBs and due to their random pathing you could even arrange a ''fishing'' setup for long term cave cleaning.
I opened up my caves,created a set of two drawbridges with spiky rooms beneath them and a pathing option around them to make the FB's path through the second room if I ever had a really dangerous syndrome FB, turned out that due to ''random pathing'' every once in a while an FB would just path into my first, open spikes room with no reason to go in there whatsoever.
I had about 10 fb's strolling around in a 3layer deep cavern and without any baits out i would kill or cripple atleast one of them per season. if you use bait you can get rid of them all in seconds. just make sure to utilize ''clean all'' in df hack if you intend to just walk in there after the killing; deadly blood and dust/etc are still lethal after the fb is removed.
also; make sure to either manually dump or autodump destroy the corpses, due to a bug butchering FB remains currently causes a noticeble drop in fps.
in my fort of 180 dwarves I am at 110-130 fps after 35 years, while just butchering 1 FB dropped that down to 80 and there was no way, apart from savescumming, to repair that.
I was about to go and call that their biggest weapon right now, till a simple deadly dust spray attack paralyzed all squads close to it
oh and, if you're really desperate and willing to use dfhack; use the liquids command and obsidianize the shit out of them. tends to get quite messy but it works!