Hello Good People

I have a 1995 E320 W124 with a 722.369 transmission. It is rebuilt. Correct fluid level. Bowden cable is functional with correct springiness and end play. Shifter linkage is adjusted properly with new bushings.

"P", "R", "N", "2" gear selector positions work properly.
"3" and "D" will not engage 2nd gear to start out.

Requires gear selector position in "2" to get rolling. Gives smooth engagement.

Manual shift from gear selector "2" to "3" gives smooth, controlled upshifts to 3rd gear.
Manual shift from gear selector "2" to "D" gives smooth controlled upshifts to 4th gear.
Downshifts from 3rd in "3" or 4th to 3rd in "D" happen smoothly.

But: 2nd gear will not re-engage in "3" or "D". Have to manually select "2" to start out again. Then, manually upshift to "3" or "D" again.

Occasionally, there's a snap engagement, like 2nd gear is going to engage, but does not. Trans feels like in neutral

Your insights and ideas are sought, please.
Thank you!