Power_Broker:
If you use a stepper motor and a limit switch to control the spindle, you can accurately control the slack length without the need of monitoring. For more info do a little bit of googling on stepper motors. This is a very simple and reliable solution IMHO.
Yes, a stepper motor was my initial idea as well. I think it would be the least complex solution, as you mention, but I came to the same conclusion that wvmarle came to; it would take a very long time to feed out/take in any significant length of line and I'm not sure that many stepper motors would have enough torque for the payload I'm going to be lifting (about 0.6 - 1kg).
If you still think a stepper motor would work well I'd be interested to hear your argument. Thanks!