In order to extend the life of the battery, I will be driving the nixie tube at a very low voltage: 155V. This is about 10V above the maintenance voltage and a lot lower than the recommended strike voltage, but it works fine. Not only does this drop the power requirement (volts x amps!), but it also reduces the size of the anode resistor I need, and the voltage drop across it, so less of the power goes to heating up the resistor.

That said, I hit my first stumbling block. I used 2xCR1632 and the voltage rapidly dropped from 6V to less than 3V. I switched to 2xCR2032 and it was much better, but hardly encouraging. Voltage was down to around 4V after about 5 min. The power supply pulls around 50mA from the cells, which is a little bit more than the 0.2mA constant discharge current they are rated for.

Still. Here is an image of it basically working.

An alternative is to use something much beefier like a CR17345. I could draw 1500mA continuously from this, and even though it is 3V - and therefore at the limit of what my power supply will work with - it works very well. It is also rated at 1500mAh. At 3V my power supply draws 73mA, so I could get about 20 hours run time out of it. Let's say the circuitry halves that. So 10 hours. That's not bad for a piece of Jewelry.

Still, I would prefer a smaller battery, so I will keep looking.