The answer really depends on what you're really trying to accomplish.
If you're trying to create a generic proxy connection to your home network from inside this hypothetical "80 outbound only" network, then there are 2 things wrong:
1) SSL typically is hosted on 443: 80 is typically non-encrypted. Allowing only port 80 outbound guarantees that surfing from that network will get you pwned.
2) Your home router is listening to the internet on port 80, which will get it pwned.
If you're trying to create a proxy from the "80 only" network to browse the web from a different IP address, there are lots of public proxies for this already.
If you're trying to access your home PC from the "80 only" network, there are solutions like GoToMyPC and LogMeIn which do this by mediating the connection.
As a generic answer, I'd say that you should config your home router to stop listening itself on port 80 (turn off cleartext http, SSL only), then port forward 80 to 22 on your home server. Bonus points for configuring iptables on your home server to do port forwarding from 80 to 22 if browsed from the "80 only" network, and to stay on 80 for all other networks.