Realized I had almost everything I needed to build a Nixie clock.
With lots of cheating.
HV side is an old TDK backlight inverter, rectified and filtered. With the bleed resistor I'm using it floats to ~270v, and runs at about ~140v when driven with 3.3v, which is adequate if a bit low for these tubes.
HV switch is a Supertex HV5122 32-channel shift register, good to 225v according to the datasheet. The Nixie has a voltage drop of around 100v, so the 5122 should never see more than ~170v on its inputs in the worst case.
I'm trying a point to point wiring technique that ChaN invented (I think, never seen it anywhere else). The magnet wire insulation is perhaps a bit underrated for the voltages in use, so I may have to go back and re-do it with the more typical 30ga Kynar stuff if it ends up breaking down somewhere. I think it'll be ok though because only one of them should be conducting at a time, and the rest will be floating on open drains.
Green daughterboard is a GPS receiver module, because why not be accurate?
I'll probably tie this all together with an ATTiny1634; read the NMEA datastream from the GPS, extract the time field, write the appropriate bits out to the 5122. Alternately and more simply, I can implement a simple clock on the AVR and use the (theoretically pretty stable) 1pps output from the GPS to clock it.
All of this is assuming it works at all, of course.