So this is my setup: 

* We have a few machines in a LAN, used for computation, which me and my colleagues access from the outside with SSH.
* All our accounts on the LAN machines are managed and shared via LDAP (resides in the LAN, but is only accessible with SSL).
* Access from the outside is restricted through one of the machines (SSH on port other than 22 and runs Fail2Ban). Password authentication is disabled and all users use passphrase-encrypted keys when logging in from outside the LAN. Root login is also disabled throughout the network.

However, as it is common to switch from machine to machine, many users use paswordless login within the LAN. This means that if an attacker gains access to that outside-facing host, he has the same level of access throughout the LAN as the user which was compromised.

How can I mitigate this risk? What are some good practices to follow? Are there other glaring issues with my setup?