Maybe we could have a tool within the article's page that would allow users to select a picture and create a summary for the article. Some of the images that are displayed are not relevant, but otherwise it works perfectly.
Topic on Talk:Page Previews/Flow
Currently it's using an automated extract, for both the text and the image.
Re: text - creating a manual summary override, would be difficult to do cleanly and at the large scale required. For the moment, it's best to just write the lead sentence in a way that extracts well, both for Hovercards and for external search engine result-blurbs. (Eventually, it might be possible to use the Wikidata descriptions, and that would be much more efficient than duplicating essentially the same task, but currently they're intended to be very short, at 2-12 words. eg. d:Q42: Douglas Adams: "English writer and humorist".)
Re: Image - There was some discussion about making a "use this image instead" override (via template or magicword). I'll see if I can find out what happened to that... Thanks for the reminder.