Unless there is a difference in the way Google and other search engines deal with the pdf documents on sharing sites vs a blog or other site, I do think that it will be harder to rank duplicate content across multiple domains or even a single domain. The reason I say this is that as a long time user of Joomla as well as using wordpress for file sharing, it has always been best practice to make the pdf no index. Joomla has this integrated into it by default (pdf sharing of articles) and its effect on SEO has always been brought up (proponents of WP over Joomla always like to bring this up). But even in WP when you share a document that has content previews, it is best to Nix one or the other from the SEs, and if you are sharing a file, which one would be obvious.
Because you are actually wishing the pdf to be SEO friendly, you would want all of them to get the best exposure possible. Because you are also looking to widely spread each and every individual document, lack of redundancy within your content cannot be totally expelled. Try to focus on the SEO of your intros and sharing site text. I am not sure if all sharing sites even have the pdfs crawled, but I would assume that they do.
While this might not seem to be a direct answer to your question, it does simply explore some of the factors involved, and I hope it helped.
