I think the framed newspapers hanging on the wall of the Daily Planet with the "Superman Dies!" and "Superman Lives!" can be explained away in light of Rebirth fairly easily. If the new52 was really in a sense the actual post-Crisis universe with like a fresh coat of paint or a new layer of wallpaper over it, with the old universe now breaking through with lead up to Rebirth, Rebirth, and Beyond, one could say that those newspapers simply represent some of the earliest cracks. They are from the post-Crisis universe, not the new52 universe. We noticed them, because as readers, we view the panels as outside observers who perceive what is there rather than just what the characters perceive. So, we saw the newspapers that way. The characters probably didn't see them or notice them, or saw something different, because the power that had created and was trying to hold these changes together wouldn't allow them to perceive things that didn't get overwritten properly.
I don't think new52 Superman was actually killed by Doomsday, but because the pre-Crisis Superman had been, and it was such a big event for so much of Clark's world and the world as a whole, that it couldn't be totally erased. The newspapers, and any small passing references could be explained away as simply the old universe breaking through for a second and then being repressed. If a character said something about it, even directly, it could be explained that it was the old universe pressing through, and then pulsing back, having the character not only re-forget the event, but actually having the character forget what he or she just said moments before.