You could use the 1062 controller, however the amount of torque in unipolar motors (at least in the ones that we currently have in stock) may not be enough to sufficiently wind the wires tight enough, or to even turn at all once the roll gets heavier.
Using the 1063 Bipolar controller would be better suited for winding tighter and heavier rolls, although it would be more expensive. Additionally, the bipolar controller has a very fine position resolution and the drift is negligible. We use them with a 3-axis rotation platform to calibrate the PhidgetSpatials and they return to the same initial position after going through multiple full and partial rotations.
If you are set in not relying on the steps though, you could use 3520 Sharp Distance Sensor
along with the adapter board, or two 1102 IR Sensors 5mm
. These output Analog Signals depending on the distance they see and would require an ADC (such as a 1018 PhidgetInterfaceKit