There was a story in which a powerful criminal syndicate moving into Gotham set a number of deathtraps for Batman. The Penguin, realizing that if the mob was successful, they would go after him and his fellow costumed criminals for cutting into their action, rounded up the usual suspects (Joker, Riddler, Catwoman, Mad Hatter, and Silver Age also-rans Cluemaster, Johnny Witts, and the Getaway Genius) to secretly help Batman avoid the traps and run the mob out of town.
One that I’ve always wanted to see: Bruce Wayne takes in a young orphan named Billy Batson as his ward: Batman and Batson. I can see this going one of two ways:
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Under Batman’s training, Captain Marvel develops into a dark, vengeful crimefighter who eventually needs to be taken down, or
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Billy doesn’t let on that he’s really Captain Marvel. Batman trains him to become Robin. But when Batman’s methods become too violent or over-the-top, Billy slips away to become Captain Marvel to keep Batman from hurting people. Of course, it wouldn’t take Batman long to deduce what was going on, and it would become a chess game of two heroes trying to manipulate each other.
In “Superman: True Brit” by Johns Cleese and Byrne, Kal-El’s capsule landed in the UK instead of the US. One day when young Clark was playing cricket, he accidentally impaled a fellow player with a cricket bat. The fellow survived, but vowed vengeance on Clark as…the Bat-Man.
“Superman and Green Lantern ain’t got nothin’ on me…” --Donovan 
There was a well done Superman Elseworld’s called Superman:Speeding Bullets, that basically did that. Baby Kal-El’s rocket ship crashes in Gotham and he’s saved by Thomas and Martha Wayne who adopt him and call him “Bruce”. His powers actually manifest when he sees his parents murdered by Joe Chill, whom he kills with heat vision.
He grows up and becomes the Batman with superpowers who is essentially a darker version of Superman.
The main thing I didn’t like about Crime Syndicate is they’re basically saying in that universe you have to be evil to win.
The Wearing the Cape series’ main protagonist is Astra, a five-foot, 100 lb. platinum blonde Catholic schoolgirl from Chicago (well, Oak Park) with super strength and flight. She started carrying a hundred pound titanium hammer named Malleus to hit with.
Actually titanium is less dense than steel. Maybe what she (or the author) meant is something hard but really dense, like iridium alloy.
Too real?
No, good can win there, but it’s just wrong. 
It’s also been expanded into a graphic novel called “The Life-Eaters”
There was also a short-lived recurring backup feature about “Bruce (Superman) Wayne” that appeared in Superman #353, 358 and 363 (1980–'81).
Those “Bruce (Superman) Wayne” stories reminded me of a story I read decades ago in which Batman, while flying the Batplane, crossed over into an alternate reality in which a Clark Kentish looking Bruce Wayne was Superman. There was also a Lois Lane look-alike who was Vicki Vale and the Joker was a TV comedian.
Also like the whole “Amalgam” comics thing which featured DC/Marvel mash-ups like “Super Soldier”, “Iron Lantern”. and a whole lot more.
As long as we’re turning the Superman/Batman roles upside-down, here’s another:
In this version, Superman gets his powers from our yellow sun, but can only use them at night- in the daytime his body switches to “recharge” mode and he becomes non-super; and if he tried to stay on Earth’s night side indefinitely, he’d eventually run out of energy. He masks himself and tries to keep to the shadows because otherwise he’d be in too much danger of being killed during his vulnerable day time.
Meanwhile, after spending his youth and young adulthood training to become an avenger, Bruce is wondering how to best put his skills to use when one day his destiny is forever changed: A public function he’s attending is attacked by criminal terrorists, and Bruce has to publicly reveal his extraordinary fighting prowess to save innocent lives. The publicity draws out Gotham’s various freak show criminals and Bruce has to defend himself against them too. He ends up embarking on a career as the Gotham Guardian, a good Samaritan who is deputized as a police auxiliary, called in to help in emergencies that a lone cop or a Swat team can’t handle. Commissioner Gordon organizes the whole show for political publicity in the battle against corrupt officials, who don’t dare challenge Wayne’s wealth and fame.