Just for another option than the initial one, maybe a sensor in the doors to know when they are closed (magnet sliding door alarms come to mind) and a mechanical endstop the door will trip when opened.
Alternatively, what are the chances of Assn optical sensor picking up a brightly clotted strip of (paint/tape/wire) on the cable to use as a positional refrence? Place the sensor before the spool and a contrast sensor would say (silver cable: go, silver cable: go, silver cable: go.... Black stripe means stop!) (or opposite if your cable is dark..)
Bah. I missed the "tent-like" comment. I had big ol' sliding hangar doors in my head. Sorry!
Dan: I like your thinking of putting a sensor on the winch. If I understand correctly you are suggesting counting spindle revolutions. Yes, it will be easy to put one or two sensors on the tail end because it doesn't get wound, but unfortunately when the doors are open those sensors will high up in the air, attached to the original hangar door ropes.
Tom: Yes, and I would like to look into this all-electronic solution of sensing current, if it is not too difficult, for the safety aspect. Thanks for reminding me of this. In the open position there is an increasing amount of load on motor. However, towards the end of the closed position, unfortunately there is no load on the motor. Dozens of spindle turns are required to release enough slack before the doors can be latched shut. I suppose a timer might work, releasing x seconds of cable after the current stabilizes.