Qing as only a Northern dynasty?

In hindsight, the Manchu conquest of China in the 17th century was one of the more fortuitous series of events of early modern era (while the Manchu's military might was evident in the decades leading up to the conquest, Li Zicheng's rebellion and the subsequent opening of the Shanhai Pass could easily be butterflied away) and is definitively one that defined the course of history for the whole of East Asia.

Now, by 1644, the Ming were clearly in a wretched spot and the Qing were in a prime position to subjugate China. However, the Qing taking all of China was still not guaranteed, even until they reached the gates of Beijing.

According to Macabe Keliher, "Although statist ambitions are evident, the conquest of Ming-controlled China was neither a given nor a clearly stated goal for either Nurhaci or Hong Taiji. Right up to the eve of the conquest of Beijing in 1644, many in the Hong Taiji government argued for limiting territorial conquest and occupation to the north and assuming the role of a northern dynasty." Hong Taiji himself had proposed getting tribute from the Ming like the Song gave to the original Jin dynasty before just getting rid of the Ming entirely.

Say the Ming have a bit more luck than in OTL or Nurhaci has more success and the Manchu manage to get further into China earlier (but aren't quite ready to swallow an entire empire whole). How would that develop (would that particular balance be sustainable for a longer period of time)? Where would the border be (the Yangtze? Huanghe?)? Could the Ming manage to revitalize and drag themselves back from the brink? Would the Manchu avoid the complete Sinicization they experienced OTL by reducing the number of Han subjects?

In view of the above, what would China (and the rest of East and SE Asia) look like with a new North-South dynasty period?
 
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