Cheers. Now that I've been away for the night and come back to it I've got somewhere... and it's a pretty simple mistake.
The ASP.NET development server only allows connections from localhost. I think this is causing the problem, as the publishing server (which is actually on localhost) is getting connection refused errors.
I can copy the service over to a machine with IIS, but then I won't have any access to the debugging stuff, right? Can I get it to log into a file or something?