That's it! I was correct in that a current source would not be needed due to the stepped voltage inputs with the caviat that the current limiting resistor for each LED needs to be sized for the respective step voltage. In addition, the zener voltage can't/shouldn't be the trigger voltage. The trigger voltage needs to be above the breakdown voltage and away from the knee and breakdown curve. If the zeners selected are 3.3, 4.7, 5.6, 6.8, 7.5, etc. the trigger voltages should be something like 4.0, 5.1, 6.2, 7.1, 8.0.
I spent most of my time trying to use NPNs to get the circuit to work, but your solution solved all the problems I ran into.
I'll be presenting the transistor ladder circuit and a variation of the LM3914 circuit to see which one they like best.