If you've got 5 or 6 BLMs you can do timed nukes to snipe them as well. If your nukes all land close enough together and the eye dies, it doesn't even get a chance to aggro, thus you won't get any links. Haven't tried this myself, but I know you can be in casting range of the eyes and out of range of the demons so it should work in theory. Then you could just waste another sac puller, or even try sniping the time extender too.
This also works for the tower of eyes. Snipe the rightmost eye, then the one directly to the left of it and the time extender will pop, and snipe that. You can do this from behind the tower. Do the same thing when popping NMs too.
XI Wiki

