Dave,
Have you already checked with exiftool if it can discern a serialnumber in the file (I don't have an A7RII file to play with so can't verify for you)? Note though that I think chances are slim it's there. From a discussion on the exiftool forum I understand they don't seem to store the shutter count either.
The only solution I have for you is to store the serialnumber in e.g. XMP. You'll need to use exiftool for that, but copying the serialnumber from the copyright tag then becomes just a matter of running a command like: exiftool "-SerialNumber<Copyright" FILE (you'll probably want to add some more options and you need to check if the Copyright tag is the correct one (sometimes tag names differ between applications).
Cheers,
Hayo