I've succesfully caught the HTTP call that is produced when clicking the "Export story to PDF" and "Export story to PPT" in the Story context menu.
Then I tried to mimick the same call in .NET by copying and pasting the HTTP body (a huge JSON-message) to the endpoint printing/export/story/ppt. This does not seem to work as the only feedback I get from the server is "Not found".
I can see that Alexander Karlsson has already replied to someone asking the same question in August here:
is it possible to take snapshots, create story ... | Qlik Community
His response seems to be related to the .NET SDK and not the REST API... so is my approach correct or does the same answer apply here?