While I still disagree with the multiverse/universe theory of yours.
Anti-Monitor was still as strong as a Universe.
The Anti-Matter Universe was made wholly seperate from the DCMultiverse/DCUniverse.
In the beginning the Multiverse and the AntiMatter Universe were made, it was meant to be a reflection of the DCU, but instead the multiverse was made rather than the universe it was meant to be. The Anti-Matter Universe itself was whole, not split like the matter counterpart.
He had complete power over the anti-matter universe, and could draw the energy of that entire universe into himself. He even does so in the story.
So he's at least as mighty as a single universe, even by your theory.
Anti-Monitor>Eternity.
He already had the power of a universe, then was conquering the multiverse and adding it even more to his power, regardless of your interpretation that still makes him mightier than a single universe. Especially by the time his appearance in the story had happened and he had conquered all but a handful of Earths.