Kill them.
Seriously. You want to throw EI into chaos? Find 5-10 like-minded people, train up infiltrators and go assassinate a few important key figures all at the same time. When they heal up, assassinate them again. Repeat 2-3 times and that character is effectively out of action for a month.
You're joking, right?
Sure it has a great atmosphere. But that's not a Dwilight special, other islands had that, too.
Note the use of present tense for Dwilight, and past tense for other islands.