opds -- used with varios apps that can see a
feed containing the books and links. But calibre2opds can also generate an HTML catalog, which is something you'll need. Of course, you *could* just maneuver around the file tree in Dropbox, but that is no fun.
As for why it's taking so long, I don't know -- that is strange. Try asking on the calibre2opds support thread in the calibre ==> related tools subforum.
Once you have a catalog, you can put that in your Dropbox Public folder and browse to it from any web browser as an ad hoc website to download books from.