The problem is, in the home case you're telling the application to talk directly to the system running the display. For the work case, with two NATs in the way, that isn't going to work (it would also be a pretty serious security hole if it did, IIRC X sessions are not encrypted at all). You need to get the application to tunnel over the ssh connection instead; that's what the "-X" option to ssh is for. If you use "-X" you should not even need to export the display, since ssh takes care of that (as well as the port forwarding required to make X work) for you.
Edit: In a nutshell, you're making this more complicated than it needs to be. Just use "-X" when establishing the ssh connection and you're basically done! (And if that isn't working, the problem is likely at the client end, e.g. some sort of Cygwin/Win8 compatibility issue...)
If the world isn't making sense to you, you're either drinking too much or not drinking enough.