The problem with Paper ->dropbox is that their documents are not accessible. Although you can link to the files themselves, there is not way to freely access the source files (so, who know how those sources actuality look like!) from dropbox itself. That limits interactions quite a bit. I don't think that the developers of dropbox paper are intending to open up things but lets see if they open this up through API's.
For now, maybe you can interact with TaskPaper files using a variety of editors and the source files they produce through dropbox's storage. I actually interact with my TaskPaper files and produce markdown files from it and then go from Markdown to Latex to PDF's. It works great and it looks great. I can give you some of the files I use if you are interested on my process.