Does anyone know the differences between the mechanicals of these two Torqueflite shifter handles used in B and E body cars from 1970-74?

I ask because I have a 1973 Charger that will not shift down into first, but has 1970s style "ball" handle instead of the proper 1973 T-handle shifter. I am wondering whether I have an incompatible shift handle with the wrong mechanicals below.

Any help?