Now at last I can authenticate to the old system. Now at last I can connect my strange application on the old network to client P's servers in London. Now at last I can find out what TCP ports it tries to connect on (23,449,8471-8476) and make the relevant changes to the firewalls and routers within client X.
This has been done.
Now we're only waiting for client P to make the relevant changes to the filters on their routers and we can start testing the application from the new network, routing through client X's link to London.
Oh happy day. If the changes to the filters on the client P routers take too long, or there's another gotcha we haven't spotted yet, then my return home tonight is in doubt.
But we hope not.