Here’s an easy way to incent Chinese Civil War battles in 2-player Global War '36: Allow the Japanese player 3 “forced KMT attacks” per game. The Japanese player plays the CCP. But in addition, they can choose up to 3 attacks through the course of the game which they force the KMT to make. They name a territory controlled by the CCP and every single adjacent KMT unit which is able to attack that territory must move into that territory and attack that turn.
You can do some play testing of the number 3 and decide if you need that to be lower or higher. You could also bid for it. “I’ll take the Axis with 2 forced KMT attacks.” The person with the bid for the fewest forced KMT attacks plays the Axis.
But I would scrap that and take a different approach. Your problem stems from ending Axis control of the CCP with the conditions you listed. Totally switch your thinking. The CCP is a permanent Axis power in a 2-player game. Imagine they approached the Japanese and said, “We’ll join the Axis if you guarantee our sovereignty.” They were embraced and are fascistic-commies. Japan isn’t going to declare war on the CCP in the 2-player version, because that would be like Germany declaring war on Italy. The Japanese want the CCP to become a major power and wipe out the KMT. Then, the CCP forces will invade Russia or the FEC. If the KMT allows the CCP to become a major power, then the Allies/Comintern are going to suffer the consequences. If the KMT goes hard core into defeating the CCP, then Japan may have incentive to declare war on the KMT, “coming to the aid of their allies.”
So on the Axis side you have:
Germany, Italy, Japan, CCP, Nationalist Spain
On the Comintern/Allied side you have:
ANZAC, CW, France, US, USSR, Republican Spain, KMT
Once you understand that the CCP is forever on the Axis side, then KMT wants to wipe them out. You might say that this weakens China and strengthens Japan’s position, but that’s nothing compared to the advantage given to the Comintern/Allies in their ability to work in a united fashion.