I see. The soot is certainly not typical. The next step I would take would be to try and test one of the tubes. You should be able to do this in circuit if you are careful.
First, I would use a multimeter to check that there is good ( > 170 volts) high voltage present at the anode pin with respect to earth.
Then, turning the clock off, I would attach a wire to ground that has a resistor in series. For the IN-8 at 190-170 volts, I think 20-25K should be a good current limiting resistor value.
Then, you can manually attach it to one cathode at a time to see if the digit lights up, independent of the control circuitry. If the tube does not not light, then indeed the nixie tube itself is probably the issue.
If high voltage is present and the tube works fine during this experiment, then the problem will trace back to the control circuit, which we can diagnose if that is the case.