That made utterly no difference -- I get exactly the same image with that arrangement as I do with just TransparentBsdf alone.

And on reading up on LightPath, that's the expected result. Light passing through TransparentBsdf doesn't become a transmission ray https://docs.blender.org/manual/en/2.79/render/cycles/settings/scene/render/light_paths.html so the value is always 0 https://docs.blender.org/manual/en/latest/render/shader_nodes/input/light_path.html , and everything goes to the TransparentBsdf node. Whereas if I reverse the TransparentBsdf and DiffuseBsdf nodes, nothing goes through the TransparentBsdf node and I don't get any light from the spotlight.

I think I have addressed the amount of light issue by better positioning the gobo and using a more uniformly bright image as the imagemap, but I'm still getting basically only one color. I currently have a hi-res sphere primitive as the gobo, parented to the light, positioned with xTran 0, yTran 0, zTran -0.55 (my units are Feet). I've tried scaling both the sphere and the imagemap up and down, but the projected light doesn't look anything like the image, it just looks uniformly colored.