After much flailing about, trying to figure out how to keep the site (generated with Publii, which is a nice, free, open-source WYSIWYG web site generator that easy enough even for us old guys to figure out), I found "rclone". Rclone is a wonderful utility that, among many other things, allows you to remotely sync a remote directory with a local one (in this case, Publii's output folder). It was a little confusing to set up until I read the instructions :P and found that you need to run "rclone config" and add a "destination" server along with your user-id and password (which has to be generated on Fastmail's site for each app; you can't use your normal login password). After some faffing about with command formats and file paths, I ended up with this:
rclone sync ~/Documents/Publii/sites/geektrap/geektrap-files fastmail:bill.geektrap.com/files/geektrap-files
where the first string after the sync command is the local (source) path, which contains the site files produced when you tell Publii to generate the site, and the second string is the location for the files on fastmail (which should coincide with the folder you have selected on Fastmail's "Websites" page for the root of the web site).
You can stick a
-v(for "verbose") on the command line to see what rclone is actually doing with your files.