Just to pick on this idea a bit...

Provide the option for all monks to generate a relatively small list of disposable passwords (similar to a one-time pad). The monk in question would retain this list and use each password in sequential order only when logging in from a machine in a public setting. Once he/she logs out, the password that was used is invalidated thereby rendering a sniffer/keyboard logger completely ineffective.

As often as not, I don't know ahead of time that I'll be logging in from a PAT or hotspot. So I'd first have to login "unsecurely" in order to login "securely".

This is not to diminish the fact that this is a hole.

Now, being nearly completely security-naive, does TLS get us anywhere?