Plans for the most appealing least functionally appropriate instrument.

Get a turntable, slightly broken or fully functional, whatever your price range. Swap out the motor with a stepper motor. Press a record with concentric circles instead of a spiral, and put different quality tones in each circle, but all just playing a440 at 33rpm. A sine track, a square track, maybe a stretched out dog bark track, whatever. Then you can, using arduino (or a basic stamp or whatever you prefer) create an input that will convert midi-inputted notes into the correct speed ratio to spin the turntable and produce any pitch you want. Like an optigan or a mellotron, but way cheaper (except the pressing vinyl part).

Alternately, for the lazy/adventurous, just put a variable resistor in place of the speed switch on the original motor. It could be a pot, or a capacitance thing (like a theremin), or some kind of string (like an ondes martenot). Whatever. That way you could get all portamento-y and wobbly and inconsistent.

This is all totally clear in my brain. If it doesn't make any sense out of my brain let me know. I'd hate to be confusing anyone.

ALSO, really the plan here is to just produce a bunch of copies of that piece of vinyl, and sell them along with maybe some plans on how folks can make the instrument themselves, and people will all go nuts with it.