There is a general pinned
Forum Discussion thread for minor issues and patch announcements, btw - but this is a slightly larger job though so I think a separate thread is useful.
Basically Twitter has "twitter tags" for this (unlike FB which does the same thing on an automated system). These are meta tags added into the top of the page that tell twitter what's in that specific page's content, which are a bit hard to write dynamically but I'm having a go. Fortunately I've been doing some PHP recently!
So far I seem to have the card set up but not the picture, I'll see what I can do about the latter...
EDIT: OK, that should hopefully be working now! They're a bit rudimentary, they just show the site logo and post title twice, but hopefully it's an improvement. I'm not sure if adding the top post on a page is possible as the longer descr, or whether that would work particularly well, but I could try that if people think it would be a particular improvement.