No doubt about it, the China campaign is one of the most annoying in the game. You're going to need mountain troops for china and marines for SE Asia and Burma. Also, since it's 1946, I'll make the assumption you're dealing with some serious superstacks.
First, what is the condition of China? i.e. is China a puppet, still fighting the Japanese, what? I'll make the assumption that Japan puppeted China since they do that in 2/3 of my games, and fail the other 1/3.
You will need to be very deliberate in your actions, hammering at key provinces from multiple angles, and taking small bites. You will also need LOTS of troops. You will probably be exceeding command limits in most battles, just due to the numbers needed in some cases. Also, try and avoid mountains (I know, yeah right!) when you can, pocketing defenders. Airpower is important, but will need to be micromanaged as superstacks in mountains do BAD THINGS to airplanes when left unattended.
Supply is the key to victory here. Your first goal should be to remove as many Japanese puppets as possible (Manchuoko, Siam, Inner Mongolia). Since you've already taken the Japanese Islands, this will then place the entire burden of supply on Nat. China puppet, and they don't have the IC to do it. Once you've knocked out the peripheries, try and go for Nat. China's IC, or if possible, isolate their capital. This will create severe supply difficulties for the Japanese and Co., and pretty soon you will reach a tipping point where their armies have wasted away enough to easily seize.
A couple other notes - the urban areas around Shanghai and your hometown can be real cast-iron Bi---es to seize, though from your description, you've already done it. Also watch out from Com China territory (or, if that doesn't exist in your version

), the three provinces to the NW of Beiping with forts and mountains. Those can be a real pain to kill.