Well, not any more. The site myfreeproxy.com looks like a very small-scale operation; it all appears to be behind a single public IP: 188.8.131.52. (There may be multiple servers behind a load balancer, but we're definitely not talking about a big server farm.) I poked at it several different ways (packet traces while using the service, repeated DNS queries, etc) and always came up with the same IP. This made blocking it trivial: drop a DENY rule in the firewalls for any traffic destined for 184.108.40.206.
I wrote the tech telling him that the hole had been plugged and to, please, let me know when the kids figure out the next free proxy service.
* Not technically our system; it's an N2H2 filtering appliance farm run by the state and we have delegated local control.