swapping the ground reference on a transformer's secondary winding
A CRT flyback makes the acceleration voltage high-voltage DC, using a combination of a step-up transformer and voltage multiplier. A copier or laserprinter corona generator works similarly. Maybe repurpose one of those?

Otherwise, what might be possible is to use such a coil to drive a Cockroft-Walton type multiplier. Here would be the first step: drive the coil. https://hackaday.com/2019/09/14/subaru-coils-make-a-great-hv-power-source/

Here's another idea: electrostatic air purifier supply, like this one: https://www.amazon.com/Voltage-Electrostatic-Cleaner-Supply-Output/dp/B073GGCFSF