I was also having the same issue with the supervised container installation. I found a solution with a simpler approach.
The supervised container for homeassistant mounts /usr/share/hassio/media to /media within the container. See the output of docker inspect -f '{{ .Mounts }}' homeassistant command.
So, in /etc/fstab, I added my “bind” mount point over /usr/share/hassio/media. My example line if /etc/fstab is here:
/home/media /usr/share/hassio/media none defaults,bind 0 0
When the docker container is started, it now sees the contents of /home/media where /usr/share/hassio/media is located, and that is what is /media within the homeassistant container.