I remember seeing some Nixie drive circuits that used 30V TTL open collector drivers. They used a 120V supply to drive the tube anode at low current, and the cathodes were connected to a pull up resistor to a 30V rail IIRC, so the drivers only had to do a pull down to ground to turn them on, and they would turn off naturally with the resistor taking the supply below extinguish voltage. Had issues with slight ghosting of segments in bright light ( photoemission on the cathodes doing that) and being a little slow to change digits, but worked well enough with no need for expensive high voltage transistors ( this was stuff designed in the 1970's, when you had TTL or discrete, and high voltage devices over 200V were expensive) abd just used the tube cathodes as switches instead.
A similar circuit was used on RADAR TR switches, though there it was more done to get speed by reducing the charge transferred into the plasma switches, they were run with a high current and this allowed them to turn on faster as they got biased just short of conduction.
The voltages Dave measured on the tube with on segments is usual, they vary according to how close they are to the lit electrode and the overlap area. Try again with a 1M pull down resistor and you will see they all will be lower, and stable. Resistor value has to be high enough to not light the off segments, so often was 1M to 4M7. With the push pull driver I would also recommend using a series low leakage high voltage diode with each segment to make them pull down only, otherwise you will have arcing inside the tube, from the ionised plasma and a high voltage on the next electrode, which is not an allowed thing and will cause ion burn at least and a burnt out tube at worst.