[@Vandy] I think atop LexCorp is the quickest and easiest way to go with it. Ultimately Lex in charge of the JLA, so having them on his doorstep makes sense, and their being there "brands" them as his. So I'd stick with that if I were you.

When/if a reformed JLA moves it'll give the move - geographically and ideologically away from Luthor - more significance.