OK, a little more weirdness to throw into the issue...
The *first* time I run the app (and attempt to upload) after the server is rebooted, it seems to work OK. Anytime after that first time, I get this error. If I reboot the server again, and try it again...once more, it works the first time, but not again after that unless I reboot the server. Is the server somehow maintaining the original open connection with the client somehow? That seems a little strange to me.
Also, the (windows) firewall on both the client and the server is turned off, so I'm guessing that's not the problem.