> It seems only a minimal set of environment variables are set 

Apparently the initial environment is empty. The values you see are defaults set by cmd.exe when it starts. It also sets the 'hidden' variable "=C:" to the current directory on the C: drive, which you can see via set "". 

As a workaround, try running the command using shell=True (i.e. cmd /c). This should let you modify the environment passed to 64-bit cmd.exe, which will be inherited by the grandchild process that it creates.