Edit: fixed. I found docker.service inside /etc/systemd/system/multi-user.target.wants/
I didn't get this to happen: "Then, systemctl start my-disk-mounter would automatically start docker and box." But that's ok. I run a manual startup script that prompts for the encryption password, mounts the disk, then starts all the systemd services. Instead of my-disk-mounter.service, I have check-that-all-disks-are-properly-mounted.service which is Required by box and docker. Thanks again.