I actually tested the firmware with a 10 based crystal (2.000 MHz). Firstly, the power savings over 4.096 MHz wasn't really worth writing home about. Saving more power would probably require further reducing the system clock frequency from 500/512 kHz, but if you do that, then you can't use an ordinary AVR programmer with an 400 kHz SPI clock. Surprisingly, the ATTiny85 retains the programmed clock divider during RESET rather than reverting to the fused divider value. So just for my own convenience, I'm sticking with 500/512 kHz, which still results in a single AA battery lasting somewhere around 6 months, if I'm doing the math right.
Anyway, after finding and fixing a minor bug, I've confirmed that the long term accuracy with a ten based crystal instead of a 2 based crystal is still good, so my fractional OCR0A mechanism works. Yay!
However, in looking at the pulse timing on my oscilloscope, I discovered something that I think I'll have to address.
Whenever you are using semiconductors to switch a large inductor on or off (this applies with motors, relays, solenoids... anything with a big coil), you need to deal with the coil collapse voltage that will be induced the moment you switch the transistor off. The usual solution is a reverse-biased diode across the coil, which will allow the diode to conduct when the coil commutates and prevent a large negative voltage from appearing at the transistor.
What I saw on the scope was that despite the presence of the diode, there was still a -1 volt pulse when the coil was switched off. Turns out, I'm using a 1N4148, and the forward voltage drop is about 1 volt.
The issue I see is that the absolute maximum section of the ATTiny85 datasheet says that the limit for any pin is -0.5 volts.
Now, to be fair, I think Atmel really means for that to apply to pins configured as inputs. It's unclear what impact there might be to an induced negative voltage spike like that on an output pin set LOW.
This was never an issue before because in most cases, I've used a transistor to switch the power on and off, and in a typical low-side NPN switching arrangement, the flyback diode is intended to keep the voltage spike under the collector-emitter breakdown voltage, which is always much higher than any reasonable diode forward voltage rating.
Fortunately, the solution is straightforward - pick a better diode. A Schottky diode can be had with a forward voltage of only 0.5 volts, and they make them in the same SOD-323 footprint. It may not - strictly speaking - be necessary to cut that spike in half given that the pin is configured as an output rather than an input, but it's probably good engineering anyway.
Also, I've added another firmware option. This one is a bit more prankish. It runs 10% fast for 12 hours, then 10% slow for 12 hours. It makes the days just fly by! For this one, it actually matters when you put the battery in. The controller has no idea where the actual hands on the clock are pointing - it's just a pulse source. So when the battery goes in, that marks the start of the 12 hour fast period.
EDIT: I asked the flyback diode question over on StackOverflow and it appears that this is not going to be a big deal. The worst case scenario is 1 volt going through a 100 ohm resistor, which would only be a potential of 10 mA on pins designed to source or sink up to 40 mA each.