On the idea of the “-site:xyz.com” trick, perhaps one could create a browser extension or a bookmarklet that would use javascript to take the URL in the browser bar and massage it to return the requisite string and then execute the appropriate search so that with a simple click of a button, anyone can “remember” how to do it?
Similarly with searching for the root URLs of particular outlets by clipping off the longer paths of URLs one could use a browser bookmarklet to accomplish this with a simple click and save the seconds involved with highlighting and pasting? The more dead simple and quicker it can be, the better off we are. I’ve documented a browser bookmarklet on my site that trims news article URLs down to the base URL: https://boffosocko.com/2017/03/27/to-amp-or-not-to-amp-that-is-the-question/
As an example of this type of functionality, albiet probably with a lot more programming and manual work, Brill’s company NewsGuard has developed a Chrome browser extension that is meant to provide visual indicators on pages and in search for levels of fact checking: https://chrome.google.com/webstore/detail/newsguard/hcgajcpgaalgpeholhdooeddllhedegi?hl=en