"Hope is the thing with feathers" - Emily Dickinson
So did I!
Taking a look at their servers and ports page (at the time of this writing) gave me the clues I needed. Try these settings with the “CardDav-sync beta” app:
|Username||Your FastMail email address, including the domain|
|Password||Your FastMail password (probably want to create an alternative login)|
That’ll get you started. Now go have yourself some fun times syncing contacts.