I managed to edit the raw height map using a free program called Krita, which can be found at:
http://www.krita.org/It was a bit of a caper to get it to work though:
To load the height file open Krita, hit "File/Open" and navigate to the folder the height map is in. In the open file window change the "All supported formats" filter to "All files". Click on your height map file and hit "Open". This brings up a "Choose Filter" window with a list of formats. In this list select "r16 heightmap" and hit "OK". This brings up a "Heightmap Import Options" window, set the size to "4096" and the button to "PC" and hit "OK".
When you are done editing it save the file as an r16 heightmap. This gives the file an "r16" suffix. Once this is edited manually to "raw" the TE loads the file successfully as a signed height map.
The only slight issue with the program is that it displays the file rotated 90 degrees to the right. This is no big deal though as it only takes a few seconds to rotate it left to match the TE orientation for editing and then back right again before saving.
IIRC I was able to create a height map in PSP, save it as a bmp, open it in Krita and then save it as an r16 file, edit the suffix to raw and open it in the TE. Like I said, a bit of a caper.