Kickdown cable adjustment or transmission problem?

1987 740 GLE
B230F
AW70 Tranny
198,000 miles
Newly rebuilt lower engine -- pulled and reinstalled.
Transmission fluids changed and filter replaced.

Symptoms: Engine runs and sounds well, transmission seems to not be up
to snuff. Upon acceleration it seemed that 1st gear was not being used
and the car was working hard to accelerate until higher speeds when it
then ran fine and shifted OK.

Treatment #1: Adjusted Kickdown cable to reduce slack (tightened
cable). Car seemed to pick up 1st gear and accelerate better, but
shifted "hard" into second.

Treatment #2: Adjusted kickdown cable, loosening the cable slightly.
Car still seemed to pick up 1st gear and accelerate better, but shifted
into 2nd and immediately into 3rd.

Treatment #3: Continued tweaking kickdown cable, and settled on less
acceleration from a stop in order to maintain smoother shifting
(avoiding hard shifts).

In sum, if I tighten the kickdown cable, I do better in 1st gear, but
shift right through 2nd and into 3rd. Perhaps by tightening the cable I
am going faster/longer in 1st than normal, thus exceeding the speed for
2nd gear and the car just goes right into 3rd?

I don't know if I need a new tranny, or need to get the kickdown cable
adjusted better. I followed Hayne's specs - 1mm distance for the crimp
to the threaded sheath at idle and ~1.99 - 2.07 inches at full
throttle. This did very little, so I began to extend the distance
assuming a stretched cable.

Would these be the signs of a worn out tranny? Not engaging 1st gear
properly? Shifting through gears?

Thanks!

 

To be clear, when I say "not engaging 1st gear", I mean it seems to be
starting off in 2nd gear and having to work harder.