I hope you are not taken ill.
Rereading your question I realized I was somewhat confused by you model (and terminology). Hence my questions. Now I think I understand what you are up to.
To make the circle (end-of-the-cable) move along a World-axis, instead of ‘Simple Constrain’ it to the spiral and add some trickery, it can better be simply given Position keyframes, making it translocate along the World’s X-axis. When you think it through its motion must be linear in space as well as in time (as long as the rotation of the spiral is linear in time), since you use an Archimedean spiral.
The spiral had 10 turns while you let it rotate 14 times (-2520° till +2520°). In order to facilitate the synchronization of spiral and end-curve, I altered the rotation in 0° to 3600 (10*360).
Experiment Spooling 001.3dm (356.6 KB)
The synchronization can even be enhanced by using an ‘Expression’ to make the end-curve move aside.
This way its movement is relative to the speed and direction of the rotation of the spiral. Hence it is easy i.e. to make the reel enroll and unroll in one go, or alter the rotation tweening
to make the rolling speed of the cable itself linear instead of exponential.
Experiment Spooling 002.3dm (475.1 KB)
Finaly in Experiment Spooling 003.3dm (344.7 KB) things get somewhat more realistic.
The spiral is truncated in the center because a start of the ‘cable’ at the very center is not only unrealistic, it also gives a distortion of the beginning of the cable.
A shrinking leading-segment is added.
The cable ends are capped.