There's also the fact that Song generally had a vigorous "civil society" (If you could call it that) that might not stand for something like that, especially the confucian scholars.
Agreed, victors in these cases often turn to the influential intelligentsia to secure their rule, and to do that they would definitely have to don the 'ruler' outfit and show some willingness not to through brute force.
Speaking of Song, it suffered from the loss of a natural geographical barrier that was the Sixteen Prefectures along with the military fortifications in the area, thus was much more subject to nomadic incursions.
I have been thinking of an earlier POD in which the Emperor Shizong of Later Zhou managed to pull off his reconquest instead of succumbing to illness at 38 (in the middle of the campaign no less). That way, the central plain would be less vulnerable to nomads (and there would be no need to plant trees around Kaifeng for strategic purposes). Of course then, Song may well be butterflied entirely out of existence, but what do you think other then that?
Btw, these are some previous threads on warring states and the three kingdoms that may be relevant to our purposes.