I would suggest /usr/local/bin because it's something built locally (inside the image) not coming from standard Alpine packages.
Yes, that's exactly what I was thinking to suggest. I saw the error about 10 tries as well, but that one I didn't fully understand- Why does the move fail exactly? Clearly the container with uid=0 has all the permissions it would ever want. My best guess is it has to do with how Docker mounts single files, so that /root/.rclone.conf is marked as "special" somehow, but I'm not sure about this. If that's the case, yes, I would agree to make a /config, set the relevant environment variable to point there, and tell the user to mount their config dir there.
Can I try a PR against https://github.com/rclone/rclone/blob/master/Dockerfile?