The Demigod League

This fanfiction will feature characters from Rick Riordan's universe and will have features of the DC universe's Justice League. First, I would like to list parallels among the Rick Riordan characters and the DC superheroes.
 * Jason is like Superman.
 * Percy is like Aquaman.
 * Frank is like Beast Boy (shapeshifting) / Martian Manhunter (haha, get it? Mars, scared of fire)
 * Nico is like Batman (I feel so, because both are sort of dark and brooding, and also Nico fitted perfectly in a Batman vs Superman parody I wrote.)


 * Hazel is like Batgirl (Except Nico is her brother, not her lover)
 * Will is like Robin (Nico's sidekick, escept Nico is his lover, not a father figure)
 * Leo could be like Lucius Fox (a young version)
 * Any skeleton could be Alfred.
 * Queen Hylla / Queen Reyna/ Thalia are like Wonder Woman (Amazons / Immortal child of Zeus)
 * Apollo's son mentioned in the Trials of Apollo, could be Green Arrow.

Now, let's make a few assumptions about this world:
 * Demigods, mortals and immortals (monsters, gods,etc.) live in peace.
 * Any demigod or monster carrying out a crime doesn't represent their whole community.
 * Alabaster has a magical ring, given to him by Hecate, which can radiate powerful beams of energy.
 * Beckendorf is still alive, but has an almost fully bionic body.
 * Connor Stoll has a boon from his father Hermes to run superfast.

Then other parallels with the Justice League would be:
 * Alabaster is the Green Lantern
 * Beckendorf is the Cyborg
 * Connor is the Flash

Could someone help me with turning it into a Riordan universe version of Batman vs Superman and the Justice League? Thanks.