Is it possible to access SSH/FTP through port tunnelling or proxy or something?

I'm not exactly sure what i'm asking for but the problem i'm facing is: i want to access my home NAS (linux) box from work. However my works proxy is pretty much locked down i can't ftp, ssh, ftps.. everything is pretty much blocked.

I can WebDAV into the box, as expected as this is port 80.. so is there any way i can access ssh/ftp over port 80? Obviously i can't listen on port 80 since it's already in use but i can change the ports to anything else not in use.

WebDAV would be suitable but since it treats all files like http requests it's hard to do web development from the box, if there is an error in the PHP file. then opening the file will just display the error, rather than the code. It's the same with .htaccess files and such, they are blocked from direct http access.

I'm not sure if either solution would be possible:
- Make WebDAV work like FTP... may be some apache configs or something?
- Port tunnelling or some sort of service to allow access to FTP/SSH over a proxy?

I don't need a lecture about trying to go outside of company networks, policies or going around firewalls. I manage the whole network it is the external firewalls whats blocking but the guys who manage it are a nightmare ignore emails and never get the job done. I've been complaining about FTP access for years as we struggle to update our own website, they say it should work, logs say otherwise.. They haven't given me full access to the proxy firewall, even though they should, i've given up trying and want to see if there is another method?