Oh well, another case of works-for-me perhaps. It is a single queue, so me sharing a link there might have filled it up - I often have to wait a minute but just before posting that link I got in immediately.
I would normally post a link to a page snapshot at archive.is, but for this particular site the author is keen not to have any copies made anywhere. Which is a shame, as the site will die eventually.
Interesting. Now, after 2am, there was no waiting. The black window came up immediately! I really do hope it will work soon. That looks pretty valuable to anyone with a website.