Again though I just think simple is best.  Set up a reality where in it New York City is still what it is, but now Boston is Metropolis, Chicago is Gotham, say Philadelphia is Star City, and St. Louis is Central City.  The avengers are SHIELDs big group that are government funded, and considered the official superhero team.  Though the heroes that want nothing to do with SHIELD for whatever reason branched off and made the Justice League.  Where they're operating privately and funded in secret by Wayne Industries.  So while they would be considered a renegade group and some groups and people, like of course J Jonah Jameson, want SHIELD to arrest the justice league.  SHIELD realize the good they're doing for the most part and are just going to wait until the justice league give them a reason to be arrested.  Of course leading to a very uncomfortable tension between the two teams on the rare occurrence they work together.