It has become pretty clear that I need at least a C123 battery to be able to deliver enough current. So I programmed up the ATTiny84 and set my breadboard power supply for 3V. I wired it all up and, bingo, it worked!

Then I tried it with the battery and it didn't work so well - the nixie didn't count properly, sometimes it display several digits at once.

Checking the voltage, the battery was being pulled down to 2.8V. Frankly I am amazed that the HV power supply worked at that voltage, however it was fine. The problem turned out to be the K155ID1. I swapped it for an old 7441 I had lying around, and everything worked just fine. Both of these are TTL devices, so 3V is pushing it. I also tried some other K155ID1 I had lying around, in case it was individual variation, but they don't work either.

I will try it with the actual 14 pin SOIC copy that I got from ebay and say how it handles the low voltage. Otherwise I will either have to use a 14 pin DIP 7441 or find a suitable lithium ion battery to use instead - but they tend to be quite large (relatively).

I'll leave you with a piccy:

In reality, the tube is counting.