Apparently the temperature coefficient of voltage of the zeners is not bad enough to bother your system. That's the main issue. If someone wants to retrofit a modern part into a legacy circuit, I'd usually want the new system to perform as well as the old.
As I recall, a 75V zener has a positive coefficient of about 0.12% per degree C, so if the internal temperature of the unit increases 30 degrees, that results in the regulated voltage changing 3.6%. On a 150V regulator that translates to a drift of 5.4 Volts (all other things not changing) so maybe that's not too bad. To be more precise, the 5V zener diode reduces the drift slightly but probably less than the uncertaintly of the temperature drift of a random diode. If the internal temperature changes more than 30 degrees so will the output change more than 5.4 Volts.
I am not criticizing this design but I find it great fun to make such calculations as I type.
Agreed, the zener linked by DC1MC does have a slightly better temperature coefficient of 0.055 to 0.095%/degC to be fair, but it's still an order of magnitude worse than the original voltage regulator tubes, which have temperature coefficients as low as -2mV/degC
at 82V, which corresponds to a temperature coefficient of only -0.0025%/degC.
The circuit I posted (along with the circuit mawyatt posted, which is nearly identical, but with a better explanation) is I think the lowest temperature coefficient easily achievable with just a few solid-state components. Even then though, the performance isn't necessarily any better than the voltage regulator tubes. If the temperature coefficient curves of the zener diode and Vbe don't cancel out exactly (which in practice they won't), the error gets "multiplied up" by the circuit. Still though, I think this is the best solid-state high-voltage regulator circuit with a relatively small parts count (it may not be as simple as just stringing a bunch of high voltage zeners together, but I think it's worth it, especially for Bargainhunter's application of an AC voltmeter). Any voltage regulator tubes you can still find now a days (even new old stock) are nearing their end of their lives (or more likely already past their end of useful life, even if unused).