Jim, There is a letter in MPH 80, August 1955 from one of the Thought Police, relating some of the experience of taking part in the filming, so although the film is usually dated as 1956, that must be the release or premiere date, not the actual filming date, which must have been prior to August 1955.
However, don't give up the hope that your bike is a film star, as at least some of the Series Ds hung around the dealers for a very long time before being registered when purchased. One of the 1984 bikes was ridden by a dealer who could well have taken it from stock.....
Do you know the dealer it was delivered to from the factory, and when?