Hi there! Try putting the shortcode [pdf]link_to_pdf_doc.pdf[/pdf] on its own line in the text editor. no spaces or line breaks.
Based on your source code copy above the <object> elements are being broken up by <p> tags everywhere.. which MIGHT be causing your issue.
Yes, it is probably a problem to have both plugins enabled at the same time. Please disable the other one and see if that resolves your issue.