Love that idea, such a great story too.
Mine goes a little something like this...
All is good in Metropolis, Clark is happy with Lois and Superman is still doing the odd rescue, cats out of trees, workers falling at construction sites, etc. But there's been no super villain activity since JL Part Two. He has constructed a Fortress of Solutide in the artic from pieces of Krytonian tech left behind (that Lex had used in BvS) in a cave in the artic aswell as some trinkets from his superheroics.
On a normal sunny day though there is incredibly bad weather, storms raging etc and Superman has to work as hard as ever saving people, be it because of falling from buildings, cars crashing etc. A portal opens only for a brief moment in Metropolis where the Black Zero had been sucked into the Phantom Zone in Man of Steel. Superman flies down towards it as it begins to suck material through and he holds himself infront of the portal but it closes suddenly. He then looks on the ground and a man is curled up shaking, he reaches down to see if the man is OK but is shocked when he sees that it's Professor Hamilton, he sees Superman and says "hes coming" and hands Superman the Kryptonian key that was left behind in the Black Zero in MOS. Then he collapses into unconsciousness.
We then cut to Star Labs, where Hamilton is been looked over by Doctors and Scientists. Superman remains there but is told to go home and they will update him on Hamilton's condition.
However, no one can contact Superman as he is at the FOS with Lois and the Kryptonian key, he can't get it to work as he hasn't quite set his system up properly. He has his robot working on the computer to fix it. He does however have a machine that alerts to any crimes or disasters. The alert goes off and he tells Lois that he will take her home, she says no chance she's coming to. They fly to Metropolis where another portal has opened, it's again sucking things in. Superman tells people to get back as its not safe, he walks towards it and he looks with his telescopic vision out comes flying FAORA who tackles Superman to the ground. The two battle in Metropolis and as they battle, Faora begins to sweat and she ends up collapsing in Superman's arms. He also takes her to Star Labs unsure of what is going on.
They put her in a room shackled down with Kryptonian metal under red sunlight. She awakens and Superman talks to her through a glass window. She calls him a coward for not facing her in person, he tries to talk her down and asks her how she got out of the Phantom Zone. She says she will only speak to General Zod, Superman tells her that Zod is dead. She demands to know how, he says that he killed him and that he regrets it. She goes crazy, Superman steps into the room, she attacks him but it's the attack of a weak person. She ends up collapsing into Superman in tears.
Later, Hamilton is resting (in the evening) he awakes, but he's not awake he seems more like a a man in a trance. He gets out of his bed, he talks to someone, who isn't there. He pulls out what looks like another Kryptonian key only this one has a three pronged symbol on it.
He finds what looks to be a control room, he can access it via a retina (guess someone forgot to take Hamilton off the access list). He enters the dark room as the lights come on, eh walks towards a main screen. He looks at the USB and the key he has, it won't fit but the key morphs as if it's a liquid metal into the right shape. The key uploads a virus on the screen as the three pronged triangle shape appears on all screens. It also appears in the room where was, Faora sees it through the glass and she looks afraid. Superman asks her how she escaped, she says that they need to leave this planet as its doomed. Suddenly a soldier comes to the head man in charge General (?) and says that Hamilton is in the control room. Superman leaves the room with Faora and goes to the control room, the doors won't open but he pulls it open with his bare hands. Hamilton turns around and says Brainiac is coming then collapses on the floor. As he does we see liquid metal crawl out of his ear and joins up with the key, it then scurries away.
Hamilton is again taken to rest, Superman returns to his fortress where his robot has finished up sorting the console. He enters his key and before him is Jor El, they have a little back and forth. He then asks Jor El who Brainiac is, Jor El's expression turns to dread as he tells Kal of the City of Kandor. We see a flashback to Krypton of the City been taken by Brainiac's drones, Zod and his army try to fight and save Kandor but the City is bottled up, Zod vows that Krypton will take Kandor back. Jor El tells in their research Brainiac had decimate the planets he had taken samples of. Kal asks if Brainiac destroyed Krypton but Jor El says no as he probably knew the planet was already doomed. Kal asks how to stop Brainiac and Jor El says he doesn't know.
Anyway I can't really write anymore detail than that but Hamilton's loading into the computer was the beacon to bring Brainiac. Superman must find the answer to stop Brainiac himself, Brainiac invades via his drones as his Skull ship nears Earth. He ends up getting Faora to help him fight Brainiac and his drones, she does end up helping protecting people including a moment where she saves a child who thanks her for saving her. A little tear slips out of Faora's eye in this moment. By the films end Superman fights Braimiac on his ship as they figure out (via Hamilton) how to open the portal back to the Phantom Zone. Superman is pushing Brainiac's ship into the Phantom Zone and Faora helps him. Superman is going to have go into the Zone but Faora blasts him off with her heat vision as she tells him to cherish his world. Faora and Brainiac's ship (with a beaten Brainiac on board) slip into the Zone as it closes in space. Superman watches on as we cut to a newspaper praising Superman and Faora for saving Earth. The film ends with Clark and Lois going out for lunch (or something else lighthearted).