Thanks for the input, everyone!
Something about this film can makes me want to see it decorated with an arc of 8-10 potentiometers.

Maybe someday I'll figure out exactly what to do with it.
I'd love to keep it the same thickness rather than expanding it to accommodate standard stomp switches, but I'm not completely against adding a riser underneath to create extra "hidden" depth.
Also, I agree with Mark that the shape and thickness of this thing would likely preclude stealthy activation of a conventional stomp switch. I think a soft switch with supporting switching electronics would be the best way to go. I actually have a soft touch DPST off-(on), on-(off) footswitch that would fit, but the threaded bushing would stick up by a comically large amount.
Plenty of thinking to do still.
I wonder if there could be a way to create a reliable piezo element tap sensor to activate a pedal circuit....