If the SSH port is blocked, you may want to have a look at tools that do HTTP tunneling.
http://www.htthost.com/
The following site is a good walkthrough although I see that you already have all your concepts and tools together.
http://www.nocrew.org/software/httptunnel.html
http://www.kingchurch.net/~hek/projects/firewallTunnel/
You can find more references googling for
tcp http tunneling
It is very unfortunate that you have to work with such restrictions on your internet connection. I bet you that the network admin bypasses those restrictions.
I connect from work to home using X over SSH or VNC over SSH
I connect from home to work using VPN + Remote Desktop
I hope you can solve your problem and thumb your nose at your network admin.