Hey Dave.
I'm new to construct and well, netplay is indeed interesting.
Can't test yet your game online but on LAN, anyway, i've found someone experiments on Python and Blender Engine and appears it used UDP library. Dunno if it would help you or even help to change this netlibrary to a UDP aproach, below link for the experiment and basic UDP source code idea:
http://blog.mikepan.com/very-simple-2player-networking-in-python/
And a post where it all started, i think:
http://blenderartists.org/forum/archive/index.php/t-100682.html
Hope it helps in some way...
EDIT 2: I've found something like Podsixnet (i guess), but with UDP protocol support as well. Maybe you should see that one too:
http://www.pygame.org/project-Mastermind+Networking+Lib-859-.html
Edit: Seems that you can transform your TCP socket to UDP socket just changing type on plugin lines like this one:
self.create_socket(socket.AF_INET, socket.SOCK_STREAM) - this is a TCP Socket, changing to:
self.create_socket(socket.AF_INET, socket.SOCK_DGRAM) - would transform to UDP socket.
Dunno what it could implies on PodSixNet anyways, but it's a start.