Without driving it..only speculating. I have a Quarter stick in my car and swapped the valve body over to manual. I had similar issues with shifter not engaging all the way..
Also had vacuum modulator issues and sticking check balls manipulating shifts...
IMO..if fine while in Drive (automatic shifting) perhaps you could rule out the trans as the issue.
Si Vis Pacem Parabellum
1967 Starlight black PMD Engineering 400 Auto 1968 Alpine Blue 400 4 speed 1968 Verdoro Green 400 HO 4 speed 2013 1LE 2SS/RS Inferno Orange Camaro.