I’ve just found LXD to be lacking as you can’t live transfer it to a different host

It isn’t lacking… https://linuxcontainers.org/incus/docs/main/howto/move_instances/#move-instances but as with Proxmox there are details when it comes to containers. VMs can fully migrate live.

I was unable to get docker running in a unprivileged LXC container

What host OS are you running on? Did you set security.nesting true on said container?