Well sometimes I have good news, sometimes I have bad news. Tonight it's bad news.
I tried the switch idea first as it seemed the most straightforward. Well it wasn't straightforward, it took about an hour and required the use of a microscope while soldering, and it still didn't work. I think the principle is still solid with the switch, but modifying it into the existing board is easier said than done. The board was designed to be small, it wasn't designed to be easily modifiable.
So next I tried filtering the hell out of the high voltage rail and keeping the knob for a full adjustable voltage, and no dice there either. No matter how much filtering I add I can't seem to get rid of the whine, and there is of course a size constraint for a maximum of how much filtering I can add.
I'll be cutting it close for this month, but I think the best course forward may be redesigning the boards and ordering a new version. With rush shipping I should be able to get them here by the end of the month so I can take care of April orders, and I would of course get extras so I could swap them out for March orders.
EDIT: Just ordered the redesigned board. I'm still not seeing a reliable way to make it work with a pot, so this will have a switch to go between low voltage and high voltage. It should work well and work quietly, and if it doesn't I'm refunding everyone and retiring