I had some time to investigate this further, this morning.
One of the Bakfiets dealers I emailed told me that these models are based on the old "Long John" designs. This is definitely the bike from the movie. The picture comes from
LongJohn.org and purportedly dates from the 1940s. Notice that the steering is controlled by a single tie-rod.
Now I just have to decide how far I'm going to let this obsession take me. Hopefully I can kill it before it gets expensive.