Would Li Zicheng still have attacked the pass? He might have gone south instead to capture more cities. And with the Qing threat to the northeast and the empire cut off from the economic regions of the south, it still looks like Beijing falls eventually.
He most likely wouldn’t have been able to take the south,given there were still Ming armies to the South,and that Ming support was much stronger there due to the region being considerably more prosperous than the north.
As for the Manchu threat,I believe that as long as the Ming Dynasty can swallow their pride,a compromise can be arranged.
Honestly though,a better POD would have been for Chongzheng not to push Hong Chengchou into more aggressive moves during the Battle of Song-jin. Prior to his interference,Hong Chengchou actually had the advantage in the battle,and could have potentially won. Defeat in this battle meant that the Ming Empire lost most of its’ crack troops,along with Hong Chengchou. Without the destruction of this force,the Ming Dynasty could have easily wiped out Li Zicheng’s peasant army.