I know there\'s a lot of questions on SO similar to this, but I couldn\'t find one for this particular issue.
A couple of points, first:
After a lot of trial and error, followed by a stagnant period while I waited for an opportunity to speak with our server guys, I finally had a chance to discuss the problem with them and asked them if they wouldn't mind switching our Sharepoint authentication over to Kerberos.
To my surprise, they said this wouldn't be a problem and was in fact easy to do. They enabled Kerberos and I modified my app.config as follows:
For reference, my full serviceModel entry in my app.config looks like this:
After this, everything worked like a charm. I can now (finally!) utilize Sharepoint Web Services. So, if anyone else out there can't get their Sharepoint Web Services to work with NTLM, see if you can convince the sysadmins to switch over to Kerberos.