Slush.. or anyone

I am having a difficult time getting my head around the stratum stuff. I am trying to figure out if I will still be able to mine as I have been.
One of my mining locations requires that I mine Via SSH tunnels. So I setup my home router to be an SSH end-point and I run Putty on my miner and open SSH tunnels back to my home router.

So with Phoenix I mine with http://127.0.0.1:8332 which redirects via Putty to http://api.bitcoin.cz:8332 via my home router.
When running CGMiner it first connects via the above, but then gets new info and tries to connect to api-stratum.bitcoin.cz:3333.

I need to get that last connection to go out my SSH tunnel. So I setup a new tunnel http://127.0.0.1:3333 to http://api-stratum.bitcoin.cz:3333 and changed the miner address to http://127.0.0.1:3333 but that does not seem to connect.

Is stratum not connecting via http?

Any ideas how to get what I had before to work with CGMiner and Stratum?