Never mind, I’m an idiot — it’s not trying to write to the directory.
Following on from the advice in this thread, I asked of my hosting provider:
Short version: get in touch with your hosting provider and tell them you have a PHP script that needs to create (not just “edit”) and later at some point delete the temporary files it created; then tell them you need them to set the PHP / Apache user so that it can do what it needs to do in a directory with 755 permissions.
But they pointed out — quite rightly — that the directories that wp-super-cache is trying to write in don’t exist. My blog has links that look like directories, e.g. http://blog.cgpgrey.com/the-united-kingdom-great-britain-england-venn-diagram/ because of the way the permalink structure is set up.
Am I missing some obvious configuration in wp-super-cache that tells it only to write in the cache directory?