I am wondering if the Cultural Revolution did turn out to become a lot worse there would be a lot more resentment then
described in
OTL if Chiang would not use that to his advantage while invading. One way he could is if Mao tried to remain Chairman after the the Great Leap Forward. He can make deals with local government officials and discruntled generals on the mainland who, while still socialist, stiill happened to be at the rough end of the Little Red Book. President Chiang Kai-shek can present himself as a humbled and learned man from exile and willing to allow left leaning members within his government while committed to acquiring whatever he can to save his motherland from an obviously inept rule
It may not help him take over all of mainland China but the ROC could bring in the Southeast provinces such as
Hubei where actual sectarian fighting took place between rival red army regiments. As for how he would get the military hardware to do it, it would be from his former WWII foe Japan in a way they produced much of the supplies that US forces used in the Korean War. This would certainly create a sticky situation within the UN, but perhaps the US and other western powers would remain steadfast while the ROC still reprisented China on the Security Councel..