Sorry, Bats, I'm a Mole

The multiverse is in turmoil. During a mission, Amuro Toru is forced into another world, where he discovers to his horror that not only can he not go back, but to survive he has to fulfill his role in this new world's Detective Conan-style setting: Find three jobs. One on the black side, where he goes undercover as Bourbon. One on the red side, as Rei Furuya's beloved first love. And one for himself, to give his version of the gray world a place to belong. Amuro Toru: What kind of chosen-one workaholic setup is this?! Luckily, Amuro is experienced, and the world provides him with a beginner's guide. The black side's boss should be the darkness and shadow of Gotham, tough enough to take a beating and with a life force on par with an immortal cockroach. The red side's boss should be the embodiment of a hero, a fearless fighter, preferably with a tragic childhood and both parents dead. His own boss can be anyone, as long as the pay is good, the work is easy, and they can make things convenient for him. Amuro Toru: Got it. Atop Wayne Tower, dressed all in black and fully armed, he gave the shadowy figure a mysterious smile: "I'm just an unremarkable information broker. Codename: Bourbon." Outside Crime Alley, he secretly took away the Red Hood, who had blown up a criminal hideout only to get Batman's retaliation: "You can call me Rei Furuya. We're both on the side of justice." At the Iceberg Lounge, dashing and suave, he showed off his professional skills as the Emperor of Part-Time Jobs: "Hello, Mr. Cobblepot. I'm Toru Amuro, and I'd like to apply for a job as a waiter at your restaurant." Before long, Amuro Toru realized he'd chosen all the wrong sides, but he still had to follow the plot and stick to his roles. "Sorry, actually, I'm an undercover agent your son sent." "I don't want to break you two up. I want to join this family." "No way, no way. Don't tell me the boss can't make payroll?" (You can tell from the blurb that the author's sanity is in excellent shape. No need for content warnings.) Theme: No pairing is impossible, only cooks who can't make a good meal.