...and I'd probably make a sort of "JLA Reserves" with the following characters:
- Alpha Centurian- because he's such an interesting "superman-esque" replacement that sort of fills the role of Adam Strange (Man out of Time and Space), but he's a more modern creation so that you could have some interesting and new adventures with him. I'd also make him Ted Kord, the person who takes up the Alpha Centurian mantle after Forever Evil, where he was killed unceremoniously during that battle.
- Bloodywynd - who would be sort of the "Phantom Stranger" role in this new JLA team. He could provide backup for supernatural problems and he is also a handy guy to drop in a MacGuffin in the middle of a storyline. There's also this suspicion that Bloodwynd is really a disguised Martian Manhunter, but nothing is ever confirmed. Bloodwynd is really Dale Gunn, from the Detroit League (pre-Flashpoint) and an old friend of Martian Manhunter.
- Aztek - would be sort of a street-level superhuman. This would also be the identity of Snapper Carr, a former member of the (pre-Flashpoint) Silver Age Justice League.
Add two more to the roster:
Since you've mentioned a team of J'onn, Courtney, Carter, Ollie, and Cisco, why not round out the JLU with Simon and Tatsu as well. I can imagine two Japanese members (Katana and Rising Sun). Also, I'd like to see arguments between Simon and Seraph over religion.