It seemed that the diode could have been added only on purpose to remove that path, but I didn't understand why you'd care to. The discharge path then must only be through the emitter of the bjt and via the base and the 220k and also from the emitter of the bjt and via the collector and the two resistors there. Okay. So you wanted to remove the 100k from being in parallel with all that. Got it.
I kind of wonder, without thinking too closely right now about the relative value of the currents via the bjt vs the 100k, whether that's all that important to add the diode. The charge rate is through the
100k. Having a large part of the discharge also through it seems to suggest roughly equal timing at first blush. Did you find the diode really helping here?(It's cheap to add, I just wonder more if you did do the analysis first and inserted it on the basis of theory instead of practice and if you did, then I'm going to sit down and work through the details on paper to see the same reasoning. I might ask for help, if I have trouble there.)
Jon