You probably still want to put a drawbridge shutter in between a GCS and an FB if you care about preserving your GCS, because some FBs spit projectiles, and a !!GCS!! isn't good for breeding. Hence, for spider safety, I'd put a goblin across the hall (also across a fortification) from the traps, and lower the shutters just to get some webs sprayed.
I don't think that GCS webs fall. In fact, I know that clown webs can fly. I think GCS webs stick to walls, but I haven't tested them on non-level surfaces often.
The trick to getting a webbing FB into position is that you have to plan for it extensively. Basically, you never control the webbing FB directly, you just coax it into a box and drop the lid on it. (Not unlike those traps where you put candy or something in a basket held up by a stick with a string attached you see in cartoons...) If you put an buildingable artifact in an alcove with a 1-tile drawbridge to cut off view, then the next tile back is where the FB will stand to try to knock over your statue/door/whatever artifact. Set up fortifications along the walls of this dead-end, and have a drawbridge behind the FB to come up when the FB is trapped by the lure. You'll need to selectively open up the lure trap only when a webber comes by.
An alternative method to this is to go the Loud Whispers route, and kill the webber however you can, put its corpse into position, and then let a necromancer see it. Undead FBs are guaranteed to hate and try to web everything as a bonus. Make sure it's totally sealed, and you probably want shutters to keep it from webbing your workers when they collect the caged FBs.