For writing/directing a JLA movie how about... Kevin Smith?
I'm honestly kind of amazed he hasn't directed one yet. He seems to be pretty popular in the geek community, and he's had at least some success with movies, and he's written some popular comics.
I think the best way to sum up a hero is by what they do. Show them in action. Show them saving innocents, show what powers they use to do it, show their attitude and personality as they do it, show what roles they play within the team. Then follow them back to HQ and show their personalities in more depth through their interplay.
As for origins, I consider those optional. Every character has a past that shapes their actions, but not every story that introduces a new character has to explain where that character came from. We didn't get an "origin story" for Indiana Jones until the third movie and the spinoff TV series. We didn't get an origin story for James Bond until 44 years into the film franchise. Where a character came from is only important inasmuch as it informs their behavior and values now. You could show that in dialogue without flashbacks. Have Clark and J'onn have a conversation about being the last of their respective species and what it feels like to be aliens on Earth, with the differences in their perspectives coming from the differences in their histories, with Clark growing up among humans and J'onn coming to Earth as an adult. Have Barry give Hal a chewing out about how his arrogant attitude and space-cop perspective blind him to the concerns of the street-level civilians that Barry, as a crime-lab tech, has to face on a regular basis, and maybe throw in some Aladdin jokes about his magic lantern and ring. Have Diana comment on how much simpler things were back on Themyscira, growing up with the Amazons. Maybe have Hal and Bruce comment on their mutual skepticism about Diana's claims of being a product of Greek gods and myths. That way, you're revealing backstory at the same time you're doing the more important job of revealing character.
We kind of got a little bit of this in The New Frontier
. We did get origin stories for J'onn and Hal, but Batman, Flash, Superman, and Wonder Woman were all already active, and our introductions to them were seeing them in action. I thought it worked pretty well in this case, but I guess the creators of that probably had a lot more confidence in their audiences familiarity with the characters than a big Hollywood film's creators might. Honestly, at this point, I'm over the origin story. I think the vast majority of characters origins could probably be covered in 5 or 10 minutes. For me what a character does with their powers is a lot more important than how they got them.