I've been moaning to anyone who'll listen that there seems to be something wrong with Known; Micropubs could not seem to find the syndication targets. And other people had the same problem, I believe. But after a really enjoyable virtual Homebrew Web Club meeting, the problem might after all be at my end.
@zegnat created a fresh install of Known as we watched, hooked it up to Twitter, and was instantly rewarded with Quill seeing his syndication target, which it resolutely refused to do on my instance of Known. (It failed actually to syndicate, but that's a separate issue.)
So, now I need to try a fresh install myself. And as @Jeena suggested, better to do that on a new and different subdomain than risk messing everything up.
Alas, there is no way on Earth I can do this until near the end of the month.
I can wait.