For a simple, easy simulation of the bistable 555 oscillator, I turned to http://www.falstad.com/circuit/circuitjs.html
Note that I have made an executive decision here to run this portion of the circuit at 5 V. I had originally thought that I would need to use 3.3 V so that the output pulses going back to the Raspberry Pi would also be 3.3 V, but it occurred to me as I worked with the circuit schematic that I could separate the high voltage and pulse detection circuits.
Running the high voltage circuit at 5 V made more sense. It allowed me to remove a 5 V to 3.3 V regulator.
Keeping in mind that the simulated components do not match the specifications (voltage, speed) of the components I am using in the real circuit, this is not bad! I made a few changes to the simulated components:
The 15 ohm resistor became 3.7 ohms
The 10 ohm variable resistor became 1.1 ohms
The output voltage is 400.65 V
This is the source for the pictured circuit. It can be pasted into a text file and imported into the simulator.
$ 1 0.000005 12.050203812241895 46 5 50
165 192 128 288 128 2 5
g 112 416 112 480 0
r 112 336 112 416 0 220000
w 112 224 192 224 0
R 256 32 256 -64 0 0 40 5 0 0 0.5
368 800 112 800 0 0 0
r 368 192 368 256 0 1000
w 320 192 368 192 0
d 368 272 368 336 1 1
g 192 256 192 304 0
w 112 336 368 336 0
w 368 256 368 272 0
w 112 224 112 336 0
c 368 352 368 400 0 1e-9 4.537480533182084
w 368 336 368 352 0
w 112 416 368 416 0
w 368 416 368 400 0
r 368 192 432 192 0 330
w 432 192 432 80 0
w 432 80 192 80 0
w 192 80 192 160 0
w 320 160 464 160 0
t 496 192 560 192 0 1 0.6576537842884171 0.7108392596088133 100
t 528 256 464 256 0 1 -4.62152249321833 0.36501959735723116 100
w 464 160 464 240 0
w 464 272 464 416 0
w 464 416 368 416 0
w 432 192 496 192 0
w 560 208 560 256 0
w 560 256 528 256 0
r 464 160 464 80 0 100000
w 256 96 256 32 0
w 256 32 464 32 0
w 464 32 464 80 0
l 560 112 560 32 0 0.01 -0.06415441391379743
w 464 32 560 32 0
w 560 112 560 176 0
d 560 112 640 112 1 1.2
r 560 256 560 336 0 3.7
r 560 336 560 416 0 1.1
w 464 416 560 416 0
c 640 112 640 176 0 1e-8 400.46336462418805
w 640 176 640 416 0
w 640 416 560 416 0
368 320 192 320 256 0 0
r 640 112 720 112 0 4700000
r 720 112 800 112 0 100000000
o 5 64 0 4098 1280 102.4 0 2 5 3
o 44 32 0 4106 5 6.4 1 2 44 3
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