An Open Source alternative to Docker Trusted Registry is Portus from SUSE. This is a front end to a private Open Source registry that allows for fine grained control of registry access and content: it can manage users, teams, and namespaces (no, not the kernel ones). It can integrate with LDAP for authentication and offers an audit trail, and can be extended for security scanning.
For s390x, quite a few options for base images are available on Docker Hub/Docker Store these days. They vary from enterprise environments over community distributions to minimal images. This post gives an overview on what is provided by various sources.