Wouldn't a VPN or tunnelling solution be better? You pass all your traffic through a fixed port on one host, then unwrap it and use the web as though the restriction wasn't there.
To bypass this, I wrote a simple ruby script to tunnel TCP connections, while adding fake HTTP headers to get through the firewall.
https://www.torproject.org/projects/obfsproxy.html.en
https://gitweb.torproject.org/pluggable-transports/obfsproxy...
OpenVPN can use TCP, it can use UDP, it can use whatever port you like, it can even use a fixed key to turn all traffic into random noise (obfuscating protocol structures).