It's real hard. I would almost say its easier for the Communists to have a shot at national power from the cities in the late 1920s than from the country side in the early and middle 1930s.
I'll give it a try though.
I suppose the CSR could take over without Japanese intervention, over a period of years, if the Communist base areas and armies roll sixes, and the KMT central government is ground down a in a Central Plains War that lasts forever. The coalition of latter day warlords eventually cripples the Nanjing regime, maybe with the CCP delivering the killing blow, but more likely the warlord coalition doing, then falling out with each other, and then the CSR taking them out one by one.
There's another, more lazy way, but I think you would consider it cheating. - Japan does not invade China in the 1930s/1940s, but the Soviet Union does. Getting the Soviets to do that is a whole other challenge of course.