What if the court of the Song Dynasty, along with the Chinese imperial family, and their staff, among them, craftsmen, engineers, had fled and taken refuge in Japan in 1279, shortly after the Battle of Yamen, which definitely sealed the fate of the dynasty Song.
I do not know how that would be possible in this window of time, or sometime just before, and what are the actions and reactions of the shogun, the emperor and the daimyo in this scenario.