Any safety issues with shocking kids?
Having just made a Geiger counter that cranks out about 500V at very low amperage, I can offer a few things to consider . . .
It's impressive to see how well a voltage like that can travel through the body. Holding a wire in each hand or even 2 people each holding a wire and touching fingers - would give me a nice "click" on my pickup circuit.
No shock was felt, but this made me wonder about any affect the HV might have on a pacemaker. I don't know but, I'd check that out.
Also note that due to the very low current (I hope!) the 600V will be impossible to measure with a standard DMM. You will get a lower reading due to the loading. However, it looks like the op-amp takes care of that problem for you. So adjust your HV via the op-amp.
Interesting project!