I I forgot you were doing edm. The 'sparks' are metal vapor and droplets erupting from the surface as current flowing through point contacts of the edm electrode and work piece. Not exactly a spark gap. Just visible light from molten metal with no gap.The Paschen's law doesn't really apply in EDM. The gap is only ~0.001 inch and it is in oil. The electrodes form a basic capacitance that will break down when the electric field reaches a certain intensity, the break down is somewhat due to the microscopic carbon and metal contaminates in it. And even using Paschen's, 0.001 inch is pretty close to what that law states.
They do this in industry with as little as 50VDC, even though no one on the forums will believe me. What I'm building is actually 95VDC @ 15Amps. After the arc starts the current and gap voltage drops to 35 to 25VDC. Depending on the electrode size.