See: Robin 3000; Justice League 3000; Justice League 3001; Adventure Comics (1938) #373; The Flash (1987) #92, 114; Legion of Super-Heroes (1984) #42-43; Legion of Super-Heroes (1989) #12-17; Who's Who in the DC Universe #8
Green Lantern, Rond Vidar
Superman, Richard Kent Skakespeare, Impulse
Animal Man, Ennis Jahnson, Animal Lad
Manhunter, Laurel Kent, Elna Kent
Doctor Fate, Sofie and the patron spirit Hauhet
Premise: Barry Allen needs a new stable home for his meta-powered children, the Tornado Twins, and is offered to rear them in the far-off future of the 31st century by what remains of S.T.A.R. Labs and Cadmus. He's aware, of course, of the last time he attempted to settle in the future, but this is another continuity, so it should be fine. His relative past won't repeat itself, right? His plan this time is to build a team, a league perhaps, and a culture of justice his children may one day inherit. Rond Vidar is the first to join; growing up with his egotistical, manipulative, domineering father, Universo, is reason enough; but he soon finds the will to show the universe who he is. Tom Wayne reluctantly joins the League after he stumbles upon Allen working the same case. Kent Shakespeare (doctor, soldier, protector) joins for humanitarian reasons, seeking to end the spread of Lady Styx; he champions the innocent. Sofie has her own time dilemma reasons to join. Ennis is eager to show what he can do even if the Legion of Super-Heroes deem him unready. Laurel’s human identity has reclaimed her Manhunter body and seeks to fight alongside and earn the trust of legacy bearers such as Shakespeare, Wayne, and Vidar.
Notes: Rather than relaunch Legion of Super-Heroes yet again, why not continue the Justice League 3000 series and find a way to shuffle its continuity into the current Rebirth continuity in Legion of Super-Heroes (2019). The story could serve as a springboard for Legion stories that normally deal with larger interplanetary stakes and politics. The Justice League could focus on Earth/Human/Terran matters. Eventually, a new Batman (Brane) could join the League and any number of other characters, i.e. Earth-Man, a new Hawkman, Princess Xenobia, and etc.