This is a wild one. I am only about 30 per cent sure on it. But still here we go.
The most common reference we have to the Adversary is the Devil. Which would make sense, except Hell and the Outsiders hardly seem to be allies.
But one weird one was a character in the Fables comic series - called the Adversary. This character is a world-conquering totalitarian dictator, a true villain. Trying to conquer all the various Folklore world. He conquers all of the European folklore and is currently trying to conquer African and Asian folklore.
He is
Gepetto - the creator of Pinocchio. I know it is goofy and insane, but hear me out.
He creates an army of these life-like automatons and also inserts them as rulers in-place of the real ones, and initially no one can tell the difference. Through his proxies he rules worlds until he then dominates them by force.
Sounds similar to another multiverse conquering/destroying force.
This also leads to a new candidate for Cowl. Someone on the White Council. Someone innocuous. Who has been onscreen but never obvious, and mentioned here and there in passing. That person is: Klaus Schneider the Toymaker. Which makes a hell of a lot of sense considering the identity of the Adversary.
Yeah it probably isn't right. But still, what if? Very wild WAG. I know Jim probably wouldn't just rip off someone's IP so directly. But still some weird coincidences.