This has been a productive discussion, and the photographs have also been very helpful. Based upon how far forward the hole for my antenna is in relationship to the Propayne's photo of the power antenna installation shown above, I doubt that the Ford power antenna would have enough vertical room to fit between the top of the wheelhouse and the top of the rear quarter panel where my antenna is located.
As far as my question about the power source for the antenna, I offered that comment simply because the antenna's location is so odd that I wondered what else the dealership might have done as a quick fix using whatever was available from the parts department that would fit within the available space and could be done with minimal effort.
As to whether or not the location of the hole for my antenna is the original spot as drilled by the dealership, all that I can offer is that there is no obvious evidence that either rear quarter panel has been repaired or replaced such that the location of the hole for the antenna was shifted from the typical placement along the driver's side rear quarter panel. If as Bob Gaines postulates that possibly the PM-300 antenna was somehow lost (or that it wouldn't fit anyway due to the location of the antenna hole) and some fixed length antenna was installed in its place, that then begs the question as to what antenna was in fact originally installed on the car. I don't know that it would be worth going down that rabbit hole since we're talking about something a dealership did over 50 years ago.
In summary, it appears that I have two options: (1) Retain the antenna in its current location and install a period correct fixed length antenna, both of which would appear difficult to explain for judging purposes, or (2) Plug the antenna hole in the right rear quarter panel, repair the right rear wheelhouse center seam damage, and install a PM-300 antenna on the driver's side rear quarter panel in its typical location. Of the two options, I am inclined to go with option (2). Any thoughts on that approach?