Hi Dave,
According to SQLite load: just speculation.
According to not supporting Postgres user data storage in Postgres client: well, in this case the container looks more like nice flavour rather than reliable solution. Every time I will kill the docker container or there will be failure the user data will be lost. It will be good to at least mount SQLite user database as an external volume (and mention it in docker hub).
To make it production ready it should be able to handle connection to external database.
Regards,
Peter