Aw I'd written a big thing but I guess it didn't come through. Definitely use Snapper Carr as our audience character, have him be a young adult coming to terms with burgeoning superpowers and needing help.
DESPERO is my impetus; he's got it all as far as I'm concerned; space despot + interdimensional aspect. And a power-set that can counter easy victories by Martian or Superman or Wonder Woman. But while I think he's the guy, I don't think he's someone you can present alone - he's got to be part of an ensemble of villains. Or rather; a conspiracy of villains. The story begins as it does in the original JLA run with Flash encountering escaping slaves. This brings in the Flash/Superman team-up as the provider of the slaves to Despero's evil empire - which itself is just allegorical for Real World criminal enterprises - to handle KANJAR RO, the space slave-trader. At this point most of the JLA have never "teamed up" but many of them have teamed up in Brave & Bold style pair-ups. So many of them haven't met other ones, but many have, so some can vouch for others, some can't, in the ways you'd tend to expect - Flash and GL know each other. Flash and Superman have raced. Superman has met Green Lantern. Superman has met Batman. Superman has met Wonder Woman. Wonder Woman and Superman have "encountered" Aquaman. So on. Superman in particular has a stake in stopping Kanjar Ro and freeing people from slavery because he's Superman. And HYATHIS comes in at this point as XO of the Hyathis Corporation bringing the cosmic "corporate allegory" in.
The next piece of the puzzle are "space weapons" - the space arms black market that is bolstering Despero's power, and that's where Green Lantern comes in while dealing with XOTAR, the WEAPONS MASTER. And that's where Green Lantern teams up with Wonder Woman. And perhaps SATURNA is the one taking the weapons. Cameo drops for Rann and Thanagar can come through this space weapon pipeline.
There's a tangent for "just how Snapper Carr gets in contact with everybody". And that's through Robin, Dick Grayson, in a story tackling Doctor Ivo working on an "early version of Amazo" that isn't fully JLA powered yet.
So at this point we have DESPERO at the top, and his organization pulls in the ensemble of, KANJAR RO, HYATHIS, WEAPONS MASTER and SATURNA, providing impetus for Superman, Flash, Wonder Woman and Green Lantern to pull together. Batman and Martian Manhunter are teamed up as "detectives" working out an X-Files style mystery - this is where the APPELAXIAN stuff comes into play. Weird metamorphic elemental seeds of some variety with some "Invasion"/"Body Snatcher"/"Body Horror" thrown in - and their metamorphic powers are a good counter to Martian Manhunter's easy access to shape-shifting and phasing. Despero perhaps used Appelaxian crystals specifically to counter the Martian and Batman, the guy with no powers, will be the one who has to cleverly free J'onn from being taken off the board for the final blow.
At this point the story has SIX villains - Despero and his five story-linked "agents", more or less. Ivo & Amazo in a small role.
Aquaman is your wild card. Something to do with the interdimensional portals and Despero's modes of invasion or stealing people. To take Atlantis off the board, TRINO and his kind, the kind of humanoid sea-monster mer-man thing from Showcase 30, which were underwater interdimensional raiders, were already enslaving Atlantis and Aquaman was doing the whole freedom fighter thing down there. He comes in clutch with timely aid from a purple-eyed underwater street orphan kid; Garth, and repels the interdimensional invaders and is able to arrive for the final fight, which I imagine takes place in Rhode Island.
Anyway, with a mind-tyrant, slave traders, arms dealers, an evil space corporation, some ecological elemental body horror beasts and such, you've got Allegory out the wazoo, which also gives all of our Justice Leaguers a reason to get involved by way of their Civilian Identities, too.
Story ends with set-up for the next one; clues and things that tease MERLIN and FELIX FAUST and the DEMONS THREE coming in the next one, all preceding the STARRO, which is a big mystical/dimensional (Doctor Strange-esque) Lovecraftian thing with Atlantis (and Camelot) at the center of it, where ancient and cruel magicians are up to no good, their powers stop heavy hitters like Superman dead in his tracks, STARRO takes the role of eldritch Cthulhu, and the team needs the addition of Zatanna, and probably the timely help from the Nth Metal that Hawkman brings to a fight, to deal with it. You can probably squeeze Jason Blood into the mix, too.