Ah... presumably the servers set a limit for the number of connections from a single IP to keep people from doing stupid things.
But I think you're pretty much SOL if you have more than 4 machines anyway, because you don't have enough IP's to cover all your machines. Even if you were to assign public IP's to workstations (which is not a great idea), you can't have some of your workstations use private addresses and some of them use public addresses. At least not without a whole lot of reconfiguring and probably cabling/hardware changes. It would definitely be a non-trivial task. Read up a bit on IP routing and how NAT works and you can see why.