to @ nickrout and pergola.fabio I have a fix 
HA’s cover.py (that I basically copied into my_cover/cover/py and modified) itself had a change I didn’t catch.
They changed a couple of import statements to be relative to the local directory (which didn’t work for my custom cover.py), and all I had to do was to change them back the way they were before.
For example:
from . import (
changed to
from homeassistant.components.mqtt import (
All is well again.