32768Hz oscilator works now 1-1.5V. I thought about further optimizing the design to only use one hex inverter IC and found the "wenzel clock divider http://www.techlib.com/files/dividers.pdf which I really like, but I was unable to get it running reliably for varying supply voltage to provide constant divider factor of two...

• The clock itself draws an avg. current, mainly caused by the electromagnet drive
• At 50% of original speed, period time is doubled, but pulse lengh, too
• = avg current consumption does not change much if input frequency is varied
• = keep additional current consumtion at a minimum

The oscillator consumes 2-3 uA (2uA for 1V, 3uA for 1.5V). This is relatively easy to measure with a multimeter in DC mode, as the current is nearly constant (the decoupling cap makes it possible). 

How much does the clock run shorter with the added circuitcy on one battery?

There is a table of AA battery characteristics: http://www.powerstream.com/AA-tests.htm

As a rough estimation: 1Ah / 3uA = ~38 Years.

To measure the power consumption of a clock, just with a multimeter, is not as easy, because it draws pulse currents into an inductive load (which depends on the position of the constant magnet??). Calculation would base on a lot of assumption, measurement setup would involve a shunt resistor and scope, which I don't have handy right now - too much effort for an estimation.

As I have to replace my clocks batteries approx. every ~3 years (26280 hrs) , this means an avg. current of 38uA. With 41uA, run time would be 2,78 years instead of 3,  = 7% / 80 days less.

Clock power consumption measurement to follow...