This is exciting, but I'm new to Keybase and don't entirely understand it yet. How can I clone a Keybase-hosted repository on a remote server? Can gpg-agent proxy through ssh similarly to ssh-agent to allow access to GPG keys (and is that what keybase uses?), without having to store my keys on the remote server? Or would I need to create a new Keybase account just for the remote server, with that account's private keys stored on the server but at least segregated from my account's full access to communication, team-management, etc? Or would the best approach be to clone the Keybase-hosted repository locally and then push it to the remote server over SSH?
Yes, probably you need a new Keybase account just for that remote server if you want the remote server be able to do git pull after the initial git clone.
If all you need is a single git clone, and you already have a Keybase account, just do a git clone locally, and use rsync to upload the result to the remote server.
