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Well, this messy bit of work, actually worked! This is my front wall (actually, my extended wall. I had to expand my fort to do this) with a gate at the front, for security. Behind the gate is a narrow corridor, which has some cage traps. The spider, marked S, placed in the corridor, will go after the bait animal, marked A. As soon as it goes forward, it steps on the pressure plate, which opens the hatches and prevents movement, giving the spider a 1x2 moving area. Most time the spider doesn't web, but sometimes it does before it steps forward, so eventually it'll shoot some web. Eventually, one of these webs will land on one of the cage traps located behind the bait animal. The cages have some separation from the bait, because chances were very high that the bait would accidentally get caged while trying to flee.
Once the web was in place, the door, marked D, was opened. It's a stone door, set to impassable, and as soon as I unlocked it the spider walked out and re-trapped itself for handy-dandy removal to the stockpile. Then, the front gate was opened. The titan, rushing to slaughter me, ran straight into the first cage trap as pretty as you please, and was captured in a split.
I now have a functioning, re-usable titan/FB cage system. Because my fort is located with a cave nearby, the surface is naturally connected to the first cavern, which means any FB in the first cavern will path their way straight to my fort and into my waiting cage setup. I can now reliably harvest as many FB, Titans, and other nasties as I want!
For once, I won't mind a party. Urist McSlacker has organized a party at the Titan Cage!