There is no tricking here. SS/fixed is noticeably more efficient than geared.
The bet is on. Name the stakes, do the test and pay up.
If Sheldon's site was up, I could point you to his take on the issue, but you'll have to believe me as it is... or not.

(BTW, the basic flaw in the schleronomous crap is that it starts out from the (false, but that's irrelevant here) supposition that the fixed drivetrain revolves at an entirely even speed as the crank pushes your foot at every revolution, as opposed to freewheel (the author seems to think that people coast into every crank revolution... no comment). Then he tries to derive an energy gain from the even movement, which is absurd. Even if this supposition was correct, the cranks pushing your foot would obviously be an energy loss. Whatever other minute factor helps your pedaling, it would be smaller than that, so you're in negative territory. That's as much as I remember. Basically, every single step is laughably off base in that text.)