It's about the role too, if there's a global/universal team then someone whose jurisdiction is in space will be in there, not in The Just America team. Space cop go space copping and leave the earth under the atmosphere to heroes that doesn't have space jurisdiction
Zatanna can get in, but only if we don't have JLD. I personally don't like teens on adult team. So I can include Ted, but not Jaime.
So far I guess:
Batman
Green Arrow
Black Canary
Ted Kord
Ray Palmer
I don't know much about Captain Atom, but he's a patriot right? Then yeah, he's definitely in.
I don't know who's Skyrocket
Whichever Hawk that has ties to Thanagar, they're on the global team. The one that do not, can be on this team.
Speaking of global vs Just America, this America team has a base in the Hall of Justice, while the space/universe/global team gets the Satellite.