Here is a clear process, using the OpenEXR format.
Note that the screen capture compression makes the grayscale depth buffer look very banded. The actual render will be smooth.
Note, also, that my choice of only 640x640 for resolution was a weak one. Although the final image is seen rather small on Facebook, a higher resolution depth map seems to make the Facebook 3D process work better and make fewer mistakes about near v. far.
Thank you , Matt for finding this new FaceBook feature!