Like you I tried the "core" Docker to start with and it worked, but I soon wanted the add-on functionality provided by the supervisor. So I tried the unsupported "hassio_supervisor Docker", but found it unreliable - it would start for a while, but then stop for no obvious reason. I looked into it for a bit, but soon decided that a supported option was a better way to go so I set up the VM version, which has been very stable since I first got it running several months ago. I know it's an extra layer of abstraction over a docker container, but HA is a light-weight system anyway so I don't think much performance is wasted. It's still a lot faster than running it on a Pi from what I can gather anyway.
You may be aware that the HA supervisor setup uses docker itself so that might be something to do with why it's not happy running within a container. When the docker version of HA supervisor created its containers I could see and manage them within unRAID, but I don't know enough about Docker to know if this is odd. It's obviously not an issue with a VM, however if there's an option to add something to HA like an external database, then I check to see if there's an unRAID version of the docker first, so I minimise the number of dockers running inside the VM.