Calculating offset

Hello...
I have question how to solve problem with cable drive gantry. In attached image the problem is visible.
Blue is rail, red is carriage in start position and yellow is carriage in end position.
In bottom is the screw (roller) with wire wound.
So in Red position the wire is straight and thus no error. But in Yellow side the wire is angled (as its unrol from screw) and has axial component that gave error in distance. With simple pitagora theorem the error is calculated and it is calculated for few positions

So how to solve that?
-Recalculating the G code is unpractical
-Write custom kinematics - as I know I must recompile that
-Use Backlash table (can't find exactly how this work but should be done without recompile)
-Other - unknown for me

Straight Angled Delta
80.00 80.00 0.00
117.70 117.72 -0.02
155.40 155.45 -0.05
193.10 193.19 -0.09
230.80 230.94 -0.14
268.50 268.68 -0.19
306.19 306.43 -0.24
343.89 344.18 -0.28
381.59 381.93 -0.34
419.29 419.68 -0.39
456.99 457.43 -0.44
494.69 495.18 -0.49
532.39 532.93 -0.54
570.09 570.68 -0.59
607.79 608.43 -0.64
645.49 646.18 -0.70
683.19 683.93 -0.75
720.88 721.69 -0.80
758.58 759.44 -0.85
796.28 797.19 -0.91
833.98 834.94 -0.96
871.68 872.69 -1.01