Aside from that, tame creatures are notorious about their webbing attitudes. Dwarf up and get a Giant Cave Spider. If those have been modded out, then we know what your problem is.
The trick for web traps in .19 was that the creature needed a path before it would start webbing, so Y path with hatches and pressure plates became essential for making a web farm. I want to say breath attacks were changed, and don't need path, but this is what I've always worked with.
@OP: ignore this, GCS is not modded out, and the webbers are happy to spit webs at enemies without a valid path. (MW 2.h)
I have no experience with web-turrets, so I don't know if they behave any different then regular webbers. I'd think not...
My web defence uses forest spiders on the same Z level as the invaders. They are stationed behind a fortification, a raising bridge and a 1 tile wide pit. The bridges are there so I can switch the spiders "off" when needed. The spiders are walled in, so no path exists to them, and the invaders must walk the (T)raps.
WWWWW.T.
WSFBB.T.
WWWWW.T.
WSFBB.T.
WWWWW.T.
WSFBB.T.
WWWWW.T.
W=wall, F=fortification, B=raising bridge, S=spider, T=weapon traps, .=pit
It works OK, but I don't recommend this, except maybe with cage traps. I lost too many dwarves during post-siege cleanup due to webs stuck on the weapon traps.
also: Questions like this should go to the masterworks subforum.