ckiick:
Use gears!
Use a couple of gears between the capacitor knob and the potentiometer to reduce the number of turns. Then you can use a 10-turn potentiometer (which are fairly easy to find) and read it via analogRead().
I have seen 10-turn pot based rotation sensors. The cap has 73 turns but let's just say 70. The capacitance range is 7.5-350pF so if the change is linear, we have ~4.9pF / turn. On lower broadcast frequencies, at around 7 Mhz, the required stepping is 1pF so we want the capacitor shaft to be turned in 1/5th or 72 degree turns. Cap to pot, that is 70 to 10 turns, let's say we use a 7:1 reduction gear. Now, pulse the motor to turn the cap 72 degrees. That should turn the pot about 10 degrees. Is that sufficient change in resistance to cause a measurable voltage change for the ADC?
@Grumpy_Mike - With the limit switch arrangement, how do I remotely read the capacitor position?