I had the same problem with a project, but I haven't worked it out yet since I'm not working on that game at this moment.
But now that I think of it a bit; perhaps move the most important (or last, or whatever) a bit so the Y is not the same? Depends on the game your making and if that would just not be the right fit..
Maybe not change the Y position but make one of the two the prominent one with a boolean variable, possibly give them each a random time to switch?
I dunno.. Those are my two cents. I would like to know the answer to this as well!