1. Use object placement tool to put an object on each corner of the river’s origonal course, then save the xml placement file.
2. Open the xml in notepad, open Google Earth as well.
3. Open Google Earth, under Tools>Options set Show Lat/long to Universal Transverse Marcator
4. Put placemarks in the same co-ordinates as the objects, Copy & paste the corordinates from the xml file. In this case, I had to place 6 objects.
5. Draw the river’s polygon so that it ended at the placemarks.
6. Complile the KMl to bgl as normal.

This has worked well apart from a road that crosses the river, as well as a ridge in the water that stubbornly refuses to dissappear. I have noticed other ridges further upstream in Miicrosoft’s own river polygons; so maybe there is another fault not of my making.