Well, there could be one of two problems happening with the zener diode idea. One is that the leakage current of the zener below its zener voltage is too high for this application. The second is that perhaps you put the zener in backwards? Please confirm which way you put it in.
As for the leakage problem I'm not sure if there is an easy fix so perhaps this idea is not so great after all. In this case, using a 12V zener won't help.
What amount of current is flowing into the pulser when it is normally on?
The idea of adding an NPN between the uP and the 3906 is bulletproof, so its too bad you can't find a way to add a 2N3904 and one 10K base resistor. The circuit would be uP -- 10K ---2N3904base --emitter grounded --- collector to existing 10K base resistor etc.