5.8 cm = ~ 3 inches so that is ok
Because you changed the short cable I will consider that to be ok also.
How you measured it is incorrect.
When in gear with prop held, as you pull or push and as soon as resistance is felt, you make a mark. The measure between the marks.
That should be between 1/2 to 9/16" ( 12.7mm - 14.3mm) This is the acceptable error/slop.
Just to be clear, and of course I am not touching or seeing this first hand.
If the bronze part is twisted 1mm or more (and you would not be able to see this clearly) you cannot adjust the cable system to properly engage in both directions.
Do this test, Test only!!
Adjust the short cable to 5 7/8" (149.3 mm)
See if this works.
If this works, the the issue (s) are with the bronze part or the shift spool/shift crank. (shift crank is the large U shaped part that moves the shift spool in the lower unit.
I have seen older shift cranks that simply have too much movement within the spool some due to wear either on the part itself or the spool.
I am still focusing on the bronze part.
I pushed the cable in, made sure it was in gear and made a mark on the point where the plastic end meets the metal thread. Then while pressure remained on the prop I lightly pulled it outwards until resistance and made another mark. This distance is 1.8cm while testing for forward and 1.5cm for backward.













