Hi Aaron,
thanks for sharing, I knew about the flat pancake but it's the first time I've read Tesla's explanation, very interesting. From what I gathered doing the little experiment Jeremy brought up, this neutralizing function of self induction works on flat spirals due to its geometry, while applying it to a normally wound coil it is exactly like putting to coils in series, basically like one bigger coil and doesn't give that sort of gain. I see your way(or Meyers) of connecting the coils like to series coils with the load in between(wich is like your drawing only differently shown):
series.jpg
It would be interesting to know what voltage gain you have like this versus two completely separate coils. I would also like to know if there is a way of taking advantage of Tesla's find but on "normal" shaped coils
regards
Mario