I think creating a second PDF is an extra step you don't need. My K3 reads word docs when I send them via email from Google Docs, so maybe you could just save the Word Doc and grab it with the "Add Books" button on calibre, then send to your k3. Or convert to mobi and then send to your k3.
If that doesn't work, post your question on the
calibre forum. Those guys will know what to do. PDFs are notoriously hard to convert.