If so, you can reset the system to a known state by driving it in one direction long enough so that you know it has reached the end of its travel
by writing it to EEPROM, perhaps when you sense that power is about to go down
For 70 turns of the motor! That is a long time for the system to take mechanical abuse. You would be better off trying to monitor the current and seeing when it reaches its stalled value.
Sensing the power is about to go is an entire project in itself. I have done many of these when designing set top boxes and it is not easy unless the power supply is integrated into the system.
What I had in mind was monitoring the voltage at the input to the voltage regulator through a voltage divider - which means that at least the regulator is built in to the system, although the power supply could be a wall wart.
So how is a 10 turn pot going to help when the total travel of this motor is 70 turns???
Too much "hanger flying". The OP needs to clearly restate the goals of the project and clearly describe the mechanical requirements of his gizmo.
How much force is required to turn the shaft (can you turn it with two fingers)? Might be possible to use a servo to turn the shaft so you would have simple position control. Couple of ways using gearing and such that might work.http://www.servocity.com/html/gears___sprockets.html
I would still suggest a stepping motor, this will give you the precision you need and as the load is light there should not be any worry about needing positional feedback, you can just use dead reckoning. The only difficulty is in determining a reference position for this system. There have been many suggestions for this, however as you have the physical system then you can determine what would be the easiest way to do this.It could be an optical slot switch, a micro switch or even a proximity switch sensing something about the thrust of the capacitor core.The only thing you omitted is the speed you want to change this tuning at. However, I suspect this is slow given the application.