How much reverse leakage would those diodes allow? You'd need rotary switches rated for that high voltage too.
I'd get 4 digits of SmartNixie or similar nixie tube controllers that integrate control circuitry (I have 4 of the original smart nixie boards from kickstarter, and they work great). Build these. Then build the control completely separately. Not only would you be able to have much more complex behavior (ie, programmable set point, rotary encoders to adjust the time, etc), you won't have your fingers touching a switch with contacts just millimeters from the high voltage.