Could you explain what you mean by “add a slight inductance at the base of the main electrodes”?
“Inductance is the property of an electrical circuit causing voltage to be generated proportional to the rate of change in current in a circuit.”
A current divided in N paths may not divide evenly if the paths are not symmetrical. However, by adding an equal impedance to each path, the current will divide more evenly. An series inductance is an impedance at high frequencies. This is a bad idea for the main cathodes for the reason stated by the previous poster- for a maximum current per voltage the cathode inductance should be reduced.
However, if it is desired to use the tungsten pins instead of the knife edge, it might help to add inductance to the pins. The main current is through the main cathodes, not the pins, so decreasing pin current would not be as bad. Inductance in the pin effectively filters out the higher frequences of current change through the pin, so that it would take time for a current path to build up from the first firing pin to the anode, and by then the current might have started from the other pins. The inductance of each pin could be increased by bending it into a spiral.