“ The second power stroke seems to be dependent upon a lot of inefficiency in the first power stroke. Is this correct?”
Yes. At the end of normal power stroke the piston drops deeper and pulls in a bit of fresh air. The normal exhaust stroke after that becomes a second compression stroke, albeit compressing a little less than a normal compression stroke. What it’s basically doing.. per my understanding.. is spreading out the *Total* combustion time across two strokes instead of one giving the fuel a little more time and a little bit more air to burn. On paper it might mean a a little more efficiency and maybe their tests show there is measurable improvement. I don’t know.
That would seem to suggest an overly rich mixture for the first power stroke, with the excess fuel to be burned by the second power stroke.