Having convinced myself that Raymond's original suggestion can't be implemented safely, I have an alternative (arguably even more radical) proposal:

Deprecate the public concrete API functions that modify object state.

Put an underscore in front of them for internal use, have the public versions trigger a deprecation warning (not to be removed until 3.6 or so), provide a C level mechanism to easily make the equivalent of a super() call and advise that everyone switch to the abstract API in order to handle subclasses properly.