Ok, the only thing that is different in my setup is that my switch has 2 leads coming off it, so no ground/green. The way I was thinking to wire it was all the black together (as the pic shows), then all the white together, and just hook the last lead coming from the actual cord (this is only a 2-wire cord, no 3rd prong) to the white as well. So basically where you have grnd/green, that would be white instead, and be connected to the other 3 wires (1 from each socket, one from the inline switch).
Would that work?
These are highly engineered precision vehicles, the first step in diagnosing the problem is to strike the suspected offending part sharply and repeatedly with a blunt object, then re-test.