Well, I figured out how to do it, and I'm here to share. Here's a video of my sample LabView VI that reads in the GPS coordinates of the mouse over the Google Earth map, captures the position of a left mouse click, and feeds it back into Google Earth through the well known network KML file.
The Source code is available at my website here
The opens the door to new GroundStation features, like "Click and Go" during a flight. Also, it could mean the retiring of ConfigTool, as all mission planning and status could be done through a single LabView VI with Google Earth.