OK, I found the references I wanted to prove that Poggle can be solved. It seems that this game was marketed under the name Merlin's Machine, Lights Out and Orbix. The obly difference it seems is that the neighbourhood of cells along the edge and corners of the game wrapp around to the other side. (Which should suggest ideas.)
The only issue is that this kind of problem has only been looked at using wrap-around neighbourhoods.
SoI need to apply a little mental knuckle-work.
Now I just need to read the chapter.