Thanks Tim for taking the time to help. The SQL user details being used all seemed in order, so I decided it was time to try again using Ubuntu and the Bitnami stack this time.
I got very similar output but with a much more helpful debug info:
Can't connect to local MySQL server through socket '/dev/null' (111)
This suggestion of changing CFG->dbhost to 127.0.0.1 instead of localhost at least let me move on from this error to a bunch of other ones, so I gave the same trick a try on my original Mac/AMPPS config and the Behat tests are now running.