."...Batman does not work in a world wherein Superman and his mythology coexist."
This Batman is seperate stance WB repeatedly puts out there , and some fans just parrot, always bugged me.
That is exactly how you play it, and why it absolutely works. That ^ statement should be exactly Batman's POV, what he believes, and should be his reaction to Superman's appearance, as completely alien, and intrusive, to "his" established world and character.
That should be the set-up to the shared U.
Two who absolutely don't belong together, not on the same planet, not in the same city, not on the same team, yet find a bigger shared and common goal.
And that forever establishes the DCU and why it works.