I've been mostly guessing about the power consumption of the Crazy Clock controller. But today, I validated my guesses.
My Rigol DS1052E doesn't have an integration function. As Dave explained recently on EEVblog, integration is the best way to quantify power consumption when the waveform is complex. If you can graph amperage against time and integrate that, the result is energy consumed against time - mAs/s. It's not exactly analogous, because the mAs/s isn't really a rate. It's the number of mAs consumed in a second's worth of time.
I took the whole kit-n-kaboodle to work today early and performed the integration. The result was that while the controller sleeps, there's around a 1 kHz complex waveform consisting of a sharp rise to 1.25mA or so, then a decay down to 0. My Rigol scope said it was an average of around 220 µA. But is that accurate in terms of energy consumption?
The integration function over one cycle of that complex waveform reported 220 nAs (actually, it was 220 µVs, but with a µCurrent Gold set for the µA/mV scale, so change Volts to Amps and divide by 1000). Since that was over the course of 1 ms of time, it's 220 nAs/.001 sec, or 220 µAs/s - the same as the 220 µA average current reported by my Rigol.
And that makes logical sense as well. The boost converter is turning 1.5 volts from a AA battery into 3.3 volts, and the datasheet says it should be doing so at roughly 80% efficiency. The ATTiny while napping should be consuming around 100 µA @ 3.3 volts when clocked at 500 kHz. In principle, that means that the battery draw should actually be something like 275 µA, so it's probable that either my measurements are a tiny bit off, the controller is a tiny bit more frugal or the boost converter is a tiny bit more efficient. Or all 3. But it's still in very much the correct ballpark.