The way I'm picturing it, the Japanese occupy most of the peninsula in the 1590s, consolidate their gains, build up their continental forces, and invade 50 years later when the Ming collapse under the pressure of rebellion and global cooling. Maybe the PoD is Oda Nobutada surviving the incident in Kyoto and assuming his father's place, so you have a real dynastic power emerge in Japan before Ieyasu.
I suppose it's possible for the Japanese to get pretty far assuming the traitor still opens the pass...
But when the Manchus sweep in, someone's screwed.