[63corvette]

How old is the cable on the shifter linkage?
I have seen some of these lose some of their working capability over a few years time. A little flex (compression and extension) in length of this cable can be causing big problems and is very hard to find.
Also how are you checking the linkage setup.
Always set it up in high gear then check all other positions by moving the shifter and then see if the pivot on the hard tranny linkage shaft is free in all the positions by pulling the linkage off the tranny hard linkage in each position. If not you have it in the wrong hole for the shifter or your cable is not solid enough to work in all the positions. The detent inside the tranny will keep it in the right places in all the positions except park where the spring loaded linkage holds the paw in the gear set outside ring.
Hope this helps.
My 2 Cents