jeffrizza:
Thanks for the suggestion. I will look into that. However, someone who responded to my post about this on Reddit brought up the point that a line unwinding from a spindle will not unwind the same length each turn, so measuring the turns of the spindle wouldn't be the best way to do this.
But you could also count revolutions with an encoder and use the line thickness to calculate (the constantly changing) spool diameter and therefore how much line goes out for each revolution. Is there some way to insure the line is evenly laid across the spindle? If so, a distance sensor mounted to examine the spool could provide a number by which to calculate the amount of line on the spool à la figure H.6.
.02