People seem to be able to reconcile the difference between cartoons, comic books, television shows, and movies easily enough. 8 year olds that watch cartoons don't seem to be bothered by different interpretations, why should we worry about teenagers?
To me, the easiest way is to a) make it continuity neutral b) demonstrate through story that this is different, a scene of Batman fighting Ra's al Ghul, both played by different actors, and his plot not involving a microwave emitter would probably due the trick as an opening, or c) rely on public relations to inform the public.
If JL is a good movie, people will either figure it out or won't care as anything more than a point of curiousity.