My Dutch friend, Eric Ruijssenaars, a professional genealogist, has answered the question of why Jansen was sometimes spelled Janssen or even Janssens. To quote from a recent email:
Both [Jansen and Janssen] mean “son of Jan.” In 1811 all people had to adopt an official surname. So this is how they registered themselves. (There’s also the variation of them with an s at the end.) From then on the names didn’t change. Can’t really explain the number of s’s people chose. Could be to distinguish themselves of course. Combined the variations would be by far the most popular surname in Nederland.
And so — not much of an explanation, perhaps, but as good as it’s going to get. In the Utrecht documents Steven and I saw, the name was always spelled “Jansen”.