I've got myself a DSO138 board, and did a little scope-creep-thingy by losing one day on redesigning the case for it found on thingiverse and 3d-printing.
What I've got is about 10mV amplitude, and a shape so weird there's no way I could detect the pitch using zero-crossings alone. I wasn't planning to do the MIDI tracking right away, but I had it in mind from the start.

Now that I know how much gain I need in order to bring the signal to 0-3.3V range of a microcontroller ADC I can start thinking about op amps I'm going to build into my future pickup.

I also solved the mystery of getting the signal in the apparent absence of magnetic field: I magnetized parts of some strings while playing with particularly strong neodymium magnets, and of course those parts produced variable magnetic field when vibrating. It took me a while t get why the signal changes so randomly while I was moving the coil along the strings.