I don't really know the answer to this question. So I am going to throw out some other questions that might help you.
Let me get everything straight. At your work, they block all ports except port 80 and port 443? No other ports are open, like port 25 for mail, no telnet, ssh etc...? Your ISP, at home, blocks inbound traffic on port 80? It seems odd to me that they would block inbound traffic on port 80 and leave port 443 open. I would think that the reason for blocking port 80 would be to keep you from hosting your own site. For the same reason I would think that they would also shut down port 443. Have you tried to access your webserver via https on port 443 from outside, ie...from work? And does it work?
You would have to force the ssh connection to port 443. Right? Then you would have to have ssh listening on port 443 on your linux box at home. Can you use port 443 for ssh? And can it be used along with https as long as they are not trying to use it at the same time?
These are mostly questions for my own benifit but I hope would help you out in your predicament as well.
Well, if crime fighters fight crime and fire fighters fight fire, what do freedom fighters fight? They never mention that part to us, do they?