Thanks for your reply. I have set them to what I believe to be correct...which is probably the reason it does not work 
I have set the connection server https secure tunnel as the hostname of the windows server itself (FQDN with port numbers as in the example). Likewise for the Blast secure gateway.
The security server is set to the public URL I use to connect in from externally. Should the connection server be set this way as well?
I would imagine I've made a noob mistake here somewhere.