This is not the answer you are looking for, but rather an alternative path.
In my case, I’ve been using podman on fedora as docker alternative in an AppVM. I’ve had not major issues since then.
As opposed to docker, it is daemonless and allows you to run as other users. Additionally (and the thing that should solve your problem) it stores the docker images on your user’s home
Storage root dir in which data, including images, is stored (default: “/var/lib/containers/storage” for UID 0, “$HOME/.local/share/containers/storage” for other users). Default root dir configured in /etc/containers/storage.conf.
– man page of podman
So if you use this there should be no need to play with bind-dirs. But if you choose to go this path, my advice is for you to read up on the differences between the two to see if it suits your needs.