I have a bit of a problem with your assumptions. You start from the underlying assumption that the ‘fake news’ is primarily an internet based phenomena. This assumption is false, the essential outlet for fake news is AM talk radio where opinion masquerades as facts and rumors become hard news. These are the outlets that are the genesis of ‘fake news,’ by focusing on the result, the web pages that are the final output; you miss much of the impact. The people who hear a radio program that lays out a story that sounds possibly credible, so they do an internet search, what do you know the story is on the ‘net so it must be true. I have experienced otherwise smart skeptical people pulled into the belief of ‘fake news’ through this exact channel. They may only hit the web site once or twice because once it confirms that their favorite ‘news’ personality on an opinion radio or TV show is telling them ‘THE TRUTH’ handed down to this personality and only this personality they tune all other voices out.

To capture the spectrum you need to include the opinion media that masks itself as news media either through word, action or impression. That is a much more difficult study to perform but in my opinion more valuable research.