It seems that you made an error in calculating the efficiency.
The maximum theoretical efficiency of a voltage doubler turning 1V into 1.8V is allready 90%. So the additional losses of the peripheral circuitry degrades this even more.
You're right Tom- but efficiency approaches 90% asymptotically for 1.8V out, and the 1.8V is minimum V at max load (higher at lighter loads). General point trying to make is that it seems one can build a reasonable simple pump oscillator with these sub-uA op amps. Thanks.