Start off with the shifter adjustment, then possibly shift lever bushings. After that checks out inspect the transmission mount. If the mounts are bad the drivetrain can move independently of the shift lever.
This is an area I am currently going to start on. My ‘56 will start in park. Wondering if this was purposely modified? When you Press the shifter release button on top to move the lever into any forward or reverse movement , it all moves the car but, that lever can just be slid from reverse into neutral or drive without pressing the top button. THAT goes against my OCD on manufacturers design and operation….and when I was looking for anything in the shop manual or the Fordomatic manual, there is minimal coverage. A small 4 line blurb about the spring loaded ball and detent piece. I am hoping that when I remove the cover and floor shifter, it will show me a more clear logical approach to fixing this. If someone has a clear tip to provide, I am all ears.
Since it’s too cold to hang out there more than 20 minutes, I can only sit inside and mull it over and over in my mind. Making me more anxious.
The shifter bracket has notches
so unless those notches are completely wiped or worn out
I would suspect the is an issue with the shifter knob spring or pin
Have you tried to start it in drive?
They make a neutral safety switch that also allows you to start in park
I have found cars that have bypassed the neutral safety switch
Good luck with your dilemma
Keep us posted