Sadly, this seems impossible. I tried to see if I could create a script that would copy paragraph heading styles from one document to another, but there seems to be no API for getting style attributes for a heading style.
There might be a slight chance you could get something working by using only custom styles, that is, defining your very own Heading styles, for example, and have a script copy those styles from a master document to slave documents. However, once you depend on the pre-defined Heading styles in any of your custom styles, you're out of luck. In any case, using such a system will take a lot of discipline when using styles, so I don't think any such solution will be very practical.
If anyone wants to work further on this, I have shared a folder on my Google Drive.