The large cap you mentioned across the power supply lines would definitly help quiet things down.. it acts like a ripple filter keeping the power at the same level for the next firing of the plug..
If you scoped the + wire without the cap in place, you'd see an awful low voltage dip when it fires...due to the fact you are in effect stopping the R/C oscillation circuit with a dead short current draw. This is why some transistors run hot...excess current draw.
My boards now have only a 2.2uf cap to filter..it used to be 100uf at 16 volts.
I used to try for the highest and most powerful spark I could get, but have since learned that humongous RFI is the result, which killed our radio signals on our planes.. So I lowerd it to fit the needs and left it alone for the last 10 years..
Feel free to add a large value cap to the circuit for filtering in your application.

John