A quick and dirty way to reset the hours from 12:59:59 to 1:00:00 without using presettable counters is to shift the wiring of the hour counter outputs by one digit, so that the "0" output connects to the "1" numeral on the nixie, the "1" output connects to the "2" numeral, and so on. The "9" output connects to numeral "0" on the nixie. So when the counter is reset to zero, the numeral "1" is displayed. The ten hour counter outputs are wired normally, but its count input is taken from the "9" output of the previous stage. The reset signal for the hour and 10 hour counter is derived by ANDing the "2" output of the hour counter with the "1" output of the 10 hour counter.
Blanking of the leading zero is done by leaving the "0" numeral of the leftmost nixie disconnected.