I would tend to lean toward the idea that there may not be a connection, may not be real but there is no harm in contiuning to seek out answers. It's a fun topic, with possible interesting results. On the other hand there might be nothing there.
Where has Jack and Barbara been? Seems a long time since they have posted anything. Not saying Jack is the final word, but he has a wealth of knowledge.
The bottom line is - it's time for photographic proof rather than 3rd party comments. He said, she said only goes so far. The Parkers and Rudy are / were strong KF advocates so the car existed. The only questions are - was it owned by Henry and was it given to Jayne Mansfield (or transferred / sold)
One aspect I keep thinking of is wasn't Jayne Mansfield more of an early 60's B movie actress and not so much a "star" in 1954 and 1955. I think I will wikipedia her and see when she was at her height, I want to say it was 1958 to 1963ish. That might dispel a connection right there.
I believe she was killed in a 1965 Buick Electra convertible, or 1966. Again a little fact checking will tell me.