How can I turn this into an (Ableton) controller?
The hard part here is that you essentially have 216 inputs you need to read.

You could multiplex the analog pins using two 74HC4051. Analogread takes around 0.1ms, so around 2ms for all 18 knobs. Debouncing would however be pretty hard.

I'd probably go with input shift registers, and remove all the resistors. You would however need 27 8-bit shift register (3 registers per 2 knobs). 

To reduce this you could encode the rotary position into 4-bit using a diode network. That way you can use only 1 shift register per 2 knobs. So 9 in total.