Dumb question, but couldn't you just tell the OpenSSH server to use port 80 or port 443 or something and just connect like `ssh me@host -p 80`?
- it means you can't also serve HTTP on those ports (so you'd need a dedicated IP address for SSH), and
- as @charcircuit wrote, it won't resist deep packet inspection.
(But if DPI is a problem and you have a spare IP address, you could just use SSH over TLS without needing the HTTP CONNECT stuff and Apache.)