I also think it's the rare "short deck" model,IIRC it was called the "Park Avenue",they were 6 or 8 inches shorter in the back than the "regular" ones....I've only seen two of these "in person" in my life,and the last one was in a small Wrecking Yard?(It had burned underhood/inside)
I tend to agree with "Buc84". This seems to be a shortened 1961 4-door model, leaving only the short-deck "Town Sedan", style #6399C, of which only 3,756 units were built.