Your idea should work.
Finding a secure and free reliable proxy can be time consuming, so if you don't mind the uptime on your home PC you can just host your own.
There are even some scripts (
http://www.mircscripts.org/comments.php?cid=2120) that offer this functionality.
Then use that router configuration page to forward the port to your LAN ip.
Try 80, it will most likely not be blocked by your school.