I was thinking of using Cthulhu as the main antagonist in my own Delta Green campaign. My idea was taking from Pisces experiments with psychics that ended tragically after the big disaster of 1925. Cthulhu is not just some massive monster, but has powerful psychic abilities as well.
The campaign was going to begin with a shotgun scenario based around an escape psychic from a program (it could be Pisces, Mj-12, The Cult of Transcendence..anyone who might be working on tapping into psychic power). I don't remember the name of the scenario but the end has one or more investigators being drawn into the killer's mind. I was going to hint that something big and powerful was watching, slimey and dark and super powerful. Arranging things and waiting for their time....
I would probably run several scenarios based around this group kidnapped and experimenting on psychics or people with magical talent. They find that the group is basically trying to recreate the 1925 Pisces incident for their own purpose.
The finale would involve tracking down this group to a facility. The Cthulhu Now scenario 'Dreams Dark and Deadly' was the basis for it. The psychics are strapped into some sort of device to try and harness their power. However the psychic energy is enough for Cthulhu, the thing lurking behind the scenes, to act. Using the dead bodies dumped in the lake and bits of twisted metal, it forms itself into a horrible psychic energy version of Cthulhu made up of lake mud, twisted rusted metal and dead corpses. A walking stumbling horror that the PCs must stop.