Hmm are you sure they don't support the CONNECT method ? That would mean you can't use SSL at all.. setup a sniffer on your machine and dump your outgoing traffic when connecting to a secure page.. I think you'll find that most places do allow SSL to happen..
Its more likely that your tunneling programing isn't working properly.. firstly peer to peer software like Kazaa is buggy as hell.. chance are that trying to tunnel it will break its back..
If you use the CONNECT method, you won't need to set up an outside relay host.. If you want you can try to bind netcat to a local port that is allowed out.. get netcat to forward all traffic to your ultimate destination.. So if you know that SMTP port 25 is allowed out, bind nc to your machine on port 25 and tell it to relay the information to your target server as so
nc -l -p 25 | nc target.com port
This is just off the top of my head, I don't know your setup.
If you want to know where most of the good research for tunneling comes from, it comes from the Realplayer guys.. and instant messengers.. most of these guys know that their customers need some way to bypass a proxy, they give you lots of different methods.. have a look at them.
I remember having typed up a couple of really massive posts on tunneling for someone whos custom application was breaking because of a proxy.. you could search through the board and find it.
I don't suggest you try to tunnel peer to peer traffic, it probably wont work, and you'll probably get into trouble.
Other than that, as the economist Adam Smith said :
"Every man, as long as he does not violate the laws of justice, is left perfectly free to pursue his own interest in his own way, and to bring both his industry and capital into competition with those of any other man."
(replace 'industry' and 'capital' with 'bandwidth' and 'shared files')