The problem with time-traveling to save the Void is that it begs the question of why don't we time travel to stop the rest of the Rejoinings. Which would end up undoing the entire history of Source pretty much.

The 13th Shard was Flooded with Darkness before the 1st Calamity/Rejoining ever happened. It was the first time the Ascians tried to Rejoin a Shard and it went wrong since they pushed too fast on the 13th Shard. It was only after the 13th Shard became the Void that they figured out how to Rejoin Shards without causing them to be Flooded.

So if the Void ever gets fixed, I doubt time-travel will have something to do with it. As it is, the Void has the fundamental problem of not having any aether. The first hurdle that would have to be overcome would be somehow getting the 13th Shard to have it's own aether cycle again and at the moment... we've yet to find a way of creating aether out of nothing. Quite the opposite in fact...