^ TBH, Batman can still work within this story without compromising MOS2 as a sequel. Let Batman be a "third member" in the Metropolis/Metallo/Lex story. Have Lex give the Caped Crusader some of the technology to weaken Superman. Lex is betting that Superman kills Batman (thus allowing Lex to prove that Clark was the superpowered murderer) or that Batman kills/injures/gets rid of Superman-forever.
Bats should be an extremely minor part of the film, but one that adds a sense of mystery and suspense. Bruce goes to Metropolis to have a "business meeting", and hears about mysterious murders of whistleblowing journalists by a villain who is to fast for the CCTV's to catch. Batman's paranoia of Superman and his trust of Alexander Luthor's vision to repair Metropolis causes him to go all out into "detective mode" slowly piecing together Clark's secret identity.
He calculates the frequency of the locations that Superman routinely flies, and flies above (or below) superman.
Ironically, he can only attack Supes once the Man of Steel is scanning the horizon for Metallo.
Batman lays the smackdown with special gauntlets laced with synthetic Kryptonite until Supes grabs one and melts it with his eyes, being very careful to avoid scorching Bruce's hand.
Batman taunts Supes about killing Zod as well as the other journalists, before telling Clark that he knows who is really hiding behind the glasses (which allows Supes to say "You think you could hide forever-Bruce?"
Supes/Clark is able to recount some type of detail that proves his innocence, and Bruce figures out he's been played.
And then he looks at Clark with remorse, and decides that he shouldn't enter Superman's battle with Luthor. But also vows to be willing to help out, should he need it. And leaves the story. Maybe it's implied that he watches over Metallo/Luthor's next potential target ( Jimmy or maybe even Lois)
Maybe he just leaves Metropolis.
But I don't want to see him in the scene with the final encounter with Metallo/Luthor.
I want the final moments of the film to be about Clark, Luthor, and Lois.
Clark disables Metallo, but knows he can't prove Lex's guilt.
Lex is more determined than ever to stop Superman-which allows for a great sequel supervillian opportunity (notice: the MOS2 sequel would be great as a TRUE Superman/Batman film).
Cut to a happy metropolis, an emotional scene with Lois, and a "back in action" ending. And then a WW post credits teaser or something, see below.
You could have a post-credits scene with Superman/Batman looking at an unknown flying object-accompanied by footage of someone hearing a jet, looking to a distance and seeing nothing. They then show a silhouette of the famous pilot's hair