The Song Dynasty is one of those historical tear jerkers that tear at my heartstrings.
But that bastion of advancement was borne of necessity, what happens to the Song should they not be conquered but instead take back the North. Does the advancement continue in this united China or does it falter in the absence of Mongol pressure?
Conquering of Song China by the Mongols was an extremely hard process by itself. And it was often interrupted by the wars of Mongols vs Mongols as a result of disintegration of their World Empire. Sometimes a Mongol army moving South against Song turned overnight and hurried North against another pretender for the throne of the Universal Khaan. The Northern Chinese generals vassals of Kublai Khan rebelled and so on and the like.
Make the Northern and internal enemies of Khublai Khan a little bit luckier and the Song China has a
good chance to survive.
Well, better Khublai Khan stop an arrow and dead, actually conquering Song was his thing. He was unbelievingly healthy and long-living for a Chengizzid. If he is replaced by a bunch of squabbling alcoholic Borigenes then the Song is saved.
And the process of Reconquista is pretty inevitable.
As for the 'Song industrialization'... Well, if you ask me, it is highly probable, as that will be the first 'powder empire' in the history. But it is not 100% certain though.