Hey, how did you install the Global 8.1 and that too on August? I mean, is your bootloader already unlocked? If the answer is yes, then you firstly need to edit the SKUID so that the device could recognize itself as a WW unit and not a CN unit. You need root access to edit the SKUID.
I am also interested in knowing what exactly happens with Google Services? Because my understanding says that only OTA updates should be broken if you flash the global version without editing the SKUID, Play Services should work fine as they are also part of the CN ROM and works okay there too. So, when you open Play Store or any other Google app, does it fail to connect to network? Or does it fail to open up at all?