First things first here is the list of the programs you will need in order to do what I will describe further down:
$bodygroup body { studio "test3-ref" }
facing-down.bmpShould look like this after editing:
3 3.5900 7.1211 21.8750 1.0000 -0.0000 0.0000 0.0000 1.0000
3 3.5900 7.1211 16.2850 1.0000 -0.0000 0.0000 0.0000 0.0313
3 3.5900 14.3111 21.8750 1.0000 -0.0000 0.0000 0.9688 1.0000
facing-down.bmpDo this for all lines that are using the texture for the faces that are facing down.
3 3.5900 7.1211 21.8750 1.0000 15.0000 0.0000 0.0000 1.0000
3 3.5900 7.1211 16.2850 1.0000 15.0000 0.0000 0.0000 0.0313
3 3.5900 14.3111 21.8750 1.0000 15.0000 0.0000 0.9688 1.0000