Y'know, what if they just like... stopped? I don't mean because of weirdly coincidental comicbook history, but because like... of actual characterization.
Superman only wanted to stop Batman, not really kill him, but when he sees himself losing control and just about to take Bruce's life, he stops, backs up and refuses to fight anymore. Like he just can't let himself do it again. Then Bats, confused, goes up to Supes and just punches him in the face, screaming "Come on! FINISH IT!" And just keeps punching Superman who is just not responding anymore. And then Supes realizes that there's something more broken about Bruce than he realized. This isn't a vendetta, it's a death wish. Bats can't deal with the guilt of having lost not only his "work family", but Jason. And he would rather die facing an insurmountable force out of some misled justification than have to live with his pain.
Like... Supes would just talk Bats down. I dunno.