One problem I see with Theory 1 is that Hydaelyn apparently needed to send an emissary (Minfilia) to the First Shard to help bring the Flood of Light under control. Why would she need to do this, if she could interact with the First Shard as easily as she could the Source? She could clean up the Light herself, directly.

Theory 2 is possible, but we don't have any evidence one way or another.

Theory 3 is also possible, but I'd think that the less discrete among the Ascians probably would have gloated about it by now if it were true.

One possible fourth theory is that the Shards HAVE no living god within their planet. Just a lifestream, and that's it. That might help to explain why it's so easy to doom one to a Flood of Light or Darkness, if there's no built-in intelligence to regulate things. That could be the purpose Ascians have in going to these Shards - to help keep the balance long enough for the Rejoining to happen.