RS, here's a simple solution for your problem. Create a central backup server and create a filesystem for it, something like /backup and share this via NFS to your client servers. Be sure to lock down the mounting capabilities within /etc/exports. On the client, mount the NFS filesystem via /etc/fstab so it will persist reboots and set up a cronjob that runs as root to run a shell script containing your rsync commands to sync the target directory to the NFS mount. Then simply back up the central server in any number of ways..
Within /backup you can have any number of directories that are named after each server's hostname and when you mount them on the client side, you can bind to a specific folder, ie /backup/yourhost1.
This alleviates the need to make a new connection to the server each time and eliminates security risks involved with allowing root login. Your idea is convuluted and you're making it more complicated than it needs to be in my opinion.