They should do Flashpoint and by the end have something like this with the new Batman:
Except the letter is from Baffleck asking the new Bat not to give hope, or something.
With CryptiK's suggestion they could probably do that moment without Flashpoint.
If it were up to me this is how Justice League would go down, broadly:
Justice League happens, assemble the six blah blah, it's called a Mother Box blah blah, I'm Steppenwolf blah blah. The League assembles, and they defeat Steppenwolf. Then they find out he was just a messenger for things to come. Darkseid arrives, with a revived Superman as his new right hand man. Maybe he kills Cyborg right off the bat, to acquire the Mother Box within him. It's a big scramble to survive action scene.
Then you cut forward several months, and Darkseid has taken over the Earth. His Omega symbols standing where cities used to. And you see Batman, in a trench-coat meeting with the remaining Justice League. Aquaman has one arm, with a hook, because why not. Batman explains his plan - he needs to kill Superman. He's going to attain some Kryptonite he's been tracking, but it might be a trap, but it's the only chance they have. Maybe he says something to Wonder Woman about Pasithea. Then he pulls Flash aside.
"You were the one who warned me about this. I need you to go back".
"But it didn't work"
"You have to go back further. When you met me... I had lost someone... it - it broke something inside me. I pushed Superman to become what he is. When you meet me - give him this letter. Let him know that no matter what happens there's still good. He can still strive for good", or something better written than that.
Then you can have a final scene with Flash gaining speed on a thrown together cosmic treadmill, while being protected by Aquaman and Wonder Woman. Wonder Woman calls on Pasithea to give Bruce Wayne of the past a vision of his present. Then Flash finally picks up enough speed and rips through the time barrier, and it's basically the BvS scene with a younger actor as Batman - you see him startle awake from a bad dream, then Flash shows up in a burst of light. You know what, forget about the letter. He just straight up tells Bruce what future Bruce told him. And Bruce looks up at him and says "My father. That's what my father used to tell me". Or something more poignant than that.
Then Flash is pulled back through time and it's this somber moment where Darkseid shows up, flying upright, and just eviscerates them. You see Batman get cut in half by Superman's heat vision too.
Then you cut back to past Bruce. He walks up to the Robin suit with renewed determination, walks over to the Batsuit then cut to credits. Or a more interesting scene than that.
The DCEU repaired!