If you want the data on the lun accessible to all servers, the simplest is to make one of the servers a NFS server and export the data to all the other servers. This includes the home directories of the students.
But you did not tell all of it.
How are the students accessing the different servers? Do the login directly or are they using some sort of remote access, like putty, ssh, telnet.
What kind of applications are we talking about. Server applications like apache, mysql. Or more like executables they start after they logged in on the servers.
Also if the students are logging into the servers you probably want a centralised authentication system like LDAP/Kerboros, otherwise you need to sync those 1000 students over 6 servers.
Man, I really miss my VMS clusters. Life was so much simpler then.