If Yi Sun-sin dies sometime before the war, I think the Japanese would have a very good chance of being victorious. They lost largely because their supply lines were cut off by the far superior Korean navy. If Yi Sun-sin is dead, they will have lost much of this naval power (no turtle ship) the general ITTL would almost certainly be far less competent.
So if the Japanese manage to defeat the Koreans decisively, what would happen next?
So if the Japanese manage to defeat the Koreans decisively, what would happen next?