Fellas,
Let me chime in here... I have not been able to do much lately because of my travel schedule and the foul weather - much of what i need to do is paint and mother nature has not been kind. Then my air compressor went out for 3 weeks and I chased down a bad start capacitor and then my pressure washer went down and I chased down a pvc elbow to fix that, yada, yada, my wife drove through some smoke and explosive particles on an interstate and made the entire finish of our 2013 Chrysler Town and Country feel and look like sandpaper. Just got done buffing that this morning - over 10 hours on that project!!! But enough about me - let's get down to it on this shifter problem.
Photo 1
This is a 55 Ford shift shaft and lever. The "detent" in question is in good shape and is case hardened steel. Usually on these shifters you do not have a problem here. This one is in good repair and is in great shape.
Photo 2
Inside the shifter shaft is small round solid washer that is pushing against the end of the shifter lever because there is a heavy duty spring behind it. THIS IS IMPORTANT! It keeps the detent in the right place once you have moved into park, etc. Check to see that this is in place and has enough pressure on the lever (I do not know the spec, but it should surely keep it pretty tight against the lever end.)
Photo 3

Photo 4
Photos 3 and 4 are most probably where your issue lies. The case hardened end of the shift lever rides against the bottom of the steering column cup (that's what I call it anyway). You can see the flat part of the cup is intact but on an automatic 55/56 Ford column this cup is in two pieces. If you look at Photo 3 and examine the left most portion of the flat part of the cup at the top of the steering column, you can tell where the shifter shaft and where the detent at the end of the shift lever engages/disengages.
The problem: case hardened steel is riding against pot metal and the pot metal wears out. If you look closely at Photos 3 and 4 you can see where this one is getting pretty thin. People did not always pull the shift lever completely towards them to shift into Park and at times it would just slide over. That's fine if it doesn't hurt your transmission, but each time this would happen you would have case hardened steel slide against pot metal. We all know the result of that given multiplied thousands of times. If the pot metal gives way at that point then your shifter will not hold park. The metal needed to hold the detent in place would essentially be missing.
I would instruct you to look there first, especially since you have it apart right?
Can you post a photo or two? What does your cup bottom look like?